john is 7 years younger than jane. the sum of their age is 10 years ago was 55 years. how old are they now
Answer: John is 29 years old and Jane is 36 years old.
Step-by-step explanation:
There are many parts to this problem, so let's start by defining John as x and Jane as y.
We know that the sum of their age 10 years ago was 55, which gives us x+y-10=55. The reason we put -10 is because of 10 years ago. If you think about it in terms of now, 10 years back is 55, so now they would be 65 years old. So we can have either x+y-10=55 or x+y=65. For simplicity, I will use x+y=65.
We also know that John is 7 years younger than Jane, which gives x=y-7.
Luckily, we have x defined for us, so we can directly substitute that into our equation.
[tex](y-7)+y=65[/tex] [combine like terms]
[tex]2y-7=65[/tex] [add both sides by 7]
[tex]2y=72[/tex] [divide both sides by 2]
[tex]y=36[/tex]
Now we know that y=36, we can plug that into either equations to find x.
[tex]x+36=65[/tex] [subtract both sides by 36]
[tex]x=29[/tex]
This concludes that John is 29 years old and Jane is 36 years old.
I need help on these questions. They confuse me.
The graphic solution for each system of equations is given as follows:
20. (5/3, 28/3).
21. (0.205, 3.846).
22. (-1/2, -5/2).
23. (-4.615, 7.462).
How to solve a system of equations graphically?The graphic solution of a system of equations is given by the point of intersection of all the equation that compose the system.
For this problem, the systems are composed by functions of the first degree, hence they are linear functions.
For each system, the graph is traced, and then the point of intersection is identified on the graph given at the end of the answer.
Each system is traced on a different color, as follows:
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In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=76In ΔOPQ, the measure of ∠Q=90°, the measure of ∠P=76°, and PQ = 4. 1 feet. Find the length of OP to the nearest tenth of a foot. °, and PQ = 4. 1 feet. Find the length of OP to the nearest tenth of a foot
The length of OP to the nearest tenth of a foot is 16.9 ft
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
ΔOPQ is right triangle
Tan (p) = opposite/adjacent = OQ/PQ
Tan (76) = OQ/4.1
4.010 = OQ/4.1
OQ = 4.010 * 4.1 = 16.441
OP² = OQ² + PQ² = 16.441 ² + 4.1² = 287.116
=> OP = √ 287.116 = 16.944
OP≅ 16.9 ft
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What is the greatest two-digit multiple of 13
Answer:
Step-by-step explanation:
91
As you can see 91 is the largest 2 digit multiple of 13 as the next multiple is 104 which is a 3 digit number.
an elargemnet or expansion occurs when the absolute value of the scale factor is less than one true or false
Yes the statement is true.
What are scale factors in Dilation?An object is enlarged if the scale factor is greater than 1. An object is reduced if the scale factor is a fraction, less than 1. A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The description of a dilation includes the scale factor (constant of dilation) and the center of the dilation. The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.
Given here Absolute value of the scale factor is greater than 1
∴ The object is enlarged if the scale factor is greater than 1.
Hence, Yes the statement is true.
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[tex]343^{-4/3}[/tex]simplify
The value of the expression [tex]343^{-4/3}[/tex] is 1/2401.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
[tex]343^{-4/3}[/tex]
This can be written as,
1/[tex]343^{4/3}[/tex]
343 = 7³
= 1/[tex]7^{3\times4/3}[/tex]
= 1/[tex]7^4[/tex]
[tex]7^4[/tex] = 7 x 7 x 7 x 7 = 49 x 49 = 2401
= 1/2401
Thus,
The value of the expression is 1/2401.
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N is an integer such that
3n+4 <19 and 10n/n^2+16Find all the possible values of n.
N is the integer between {3,4,5}.so we can find all possible values of n is 2 and 8.
What is an integer?An integer is a whole number that can be positive, negative or zero. Examples of integers are -5, 1, 5, 8, 97, and 3,043.The integers are generated from the set of counting numbers and the operation.
What are the steps to solving inequalities?Subtract the same number from both sides. Multiply both sides by the same positive number. Divide both sides by the same positive number. Multiply both sides by the same negative number and reverse the sign.
Now we solve
3n+4 <19
3n+4-4<19-4
3n<15
n<5
so n is less than and equal to 5 it will be {3, 4, 5].
10n/[tex]n^{2}[/tex]+16 >1
10n> [tex]n^{2}[/tex] +16
0> [tex]n^{2}[/tex]-10n +16
0>[tex]n^{2}[/tex] -8n -2n +16
0> n(n-8)-2(n-8)
0> (n-8) (n-2)
So n-2<0 n-8<0
n<2 n<8
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Write the ratio of the first measurement to the second measurement. Compare in inches.
Answer:
when the ratio of the first measurment is already there, get the pot, put it in place and chec the correct ratio, the slope should help the gaurdian. so in that case, the answer is 75inch
What is the value of x in log2 x 3?
value of x = 8 as per logarithm laws.
What is logarithm?In mathematics, logarithm is an exponent or power for which a particular number is raised to achieve a required number. In other words, logarithm is a mathematical expression that states about how many times a number can be multiplied by the same number to get some required numbers.
The method of expressing any exponential relationship in the inverse form is called log notation.
What is the value of x in the question?In this question, we are given a log base 2 or binary logarithm.
given, ㏒₂ x = 3
as per the logarithm laws ㏒a y = m
y = a∧m
we write. ㏒₂ x = 3
x = 2³
hence, x = 8
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A financial analyst wants to set up a hypothesis test to determine if the mean yearly salaries of teachers, tutors, and professors are the same. What would be the correct setup for the null and alternative hypotheses for this test
Null hypothesis (H0): There’s no effect in the population. Alternative hypothesis (Ha or H1): There’s an effect in the population.
Which null and alternative hypotheses are correct?The null and alternative hypotheses are two opposing ideas that researchers use a statistical test to analyze evidence for and against: The null hypothesis (H0) states that there is no influence in the population. Alternative hypothesis (Ha or H1): There is a population effect.
Identify the null and alternative hypotheses.
As well as the sample size, specify.
Choose a suitable statistical test.
Gather information (note that the previous steps should be done prior to collecting data)
Based on the sample data, compute the test statistic.
Examine the null hypothesis, usually indicated by H0.
Always write the alternative hypothesis, which is usually marked by Ha or H1, with less than, greater than, or not equals symbols, i.e., (,>,or).
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Is (x 5) a factor of f(x) = x3 − 4x2 3x 7? explain your reasoning.
(x+5) is not a factor of f(x) because x = -5 does not satisfy the given equation f(x) = x³ - 4x² + 3x + 7.
Step 1. First we solve the equation x +5 = 0, we get
x = -5
Step 2. By putting the value of x = -5 in f(x) check whether we get a zero or a number other than zero.
If we get zero then x+5 is a factor of f(x) and if we get a number other than zero then x+5 is not a factor of f(x)
f(-5) = (-5)³ − 4(-5)² + 3(-5) + 7 = - 233
Since we got -233 and not 0. Therefore, (x+5) is not a factor of f(x).
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Find the value of x. Assume that segments that appear to be tangent are tangent.
Assuming segments that appear to be tangent are tangent, sqrt(277) = x has an estimated value of 16.64331698.
what is Pythagoras theorem ?The Pythagorean Theorem, often referred as the Mathematics, is the fundamental Euclidean geometry relationship among the three sides of a right triangle. The area of a squares with the equilateral triangles side is the sum of the surfaces of square with the other two sides, according to this rule. The Pythagorean Theorem says that the square that spans a right triangle's hypotenuse opposite the perfect angle equals the sum of the squares that span its sides. It is sometimes written as the generic algebra notation a2 + b2 = c2.
given
14 is tangent to the circle and 9 is a radius, making this a right triangle.
In order to resolve this issue, we can employ the Pythagorean theorem.
a^2 +b^2 =c^2
9^2+14^2 =x^2
81+196 = x^2
277 = x^2
Taking the square root of each side
sqrt(277) = sqrt(x^2)
sqrt(277) =x
Assuming segments that appear to be tangent are tangent, sqrt(277) = x has an estimated value of 16.64331698.
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The price of a computer is reduced by 17.5%
The reduced is £264
By how much is the price reduced
Answer:
To find out by how much the price was reduced, we can use the following equation:
price reduction = original price * reduction percentage
We know that the price reduction is £264 and the reduction percentage is 17.5%, so we can plug those values into the equation to get:
price reduction = £264 / 17.5%
To solve this equation, we need to express the percentage as a decimal. We can do this by dividing the percentage by 100:
price reduction = £264 / (17.5 / 100)
This simplifies to:
price reduction = £264 / 0.175
Solving this equation gives us a price reduction of £1512.
So, the original price was reduced by £1512.
Step-by-step explanation:
Which line L has a slope of zero?
Answer:
D
Step-by-step explanation:
GradientA Gradient is also called a slope of a line, which represents how steep a line is.
Formula of slope: Vertical difference ÷ Horizontal difference
For a slope to be zero, the line must be horizontal.
SolutionBased on the question given, we can deduce that D is a horizontal line and therefore the slope is zero.
A window is to be built in the shape of a rectangle surmounted by an isosceles
triangle. The area of the window must be 6m2. Use Lagrange Multipliers to find
the width and height of the rectangle for which the perimeter of the window will be
as small as possible. (Clarications: (1) A rectangle surmounted by a triangle has
the shape of a stick drawing of a house as might be drawn by a child, a rectangle
with a triangle on top. (2) The window's perimeter is made up of three sides of
the rectangle and the two equal length sides of the triangle. Draw a diagram! (3)
This may require some industrial strength algebra!)
The width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).
What is the Lagrange multiplier?
The Lagrange multiplier, λ, measures the increase in the objective function (f(x, y) that is obtained through a marginal relaxation in the constraint (an increase in k). For this reason, the Lagrange multiplier is often termed a shadow price.
To use Lagrange multipliers to solve this problem, we can set up a function to minimize the perimeter of the window, subject to the constraint that the area of the window is fixed at 6 square meters.
Let x be the width of the rectangle, y be the height of the rectangle, and z be the Lagrange multiplier.
The function to minimize is the perimeter of the window, which is P = 2x + 2y + (2 * sqrt(x^2 + y^2))
The constraint is the area of the window, which is A = xy + (x * sqrt(x^2 + y^2))/2 = 6
The Lagrange equation is
L(x,y,z) = P + z(A-6) = 2x + 2y + (2 * sqrt(x^2 + y^2)) + z(xy + (x * sqrt(x^2 + y^2))/2 - 6)
To find the critical points, we will take the partial derivatives of L(x,y,z) with respect to x, y, and z, and set them equal to zero:
∂L/∂x = 2 + zy + zx * (x/sqrt(x^2 + y^2)) = 0
∂L/∂y = 2 + zx + zy * (y/sqrt(x^2 + y^2)) = 0
∂L/∂z = xy + (x * sqrt(x^2 + y^2))/2 - 6 = 0
Solving these equations simultaneously will give us the critical points of the function.
We will get two critical points (x,y) = (3sqrt(2), 2sqrt(2)), (0,2sqrt(2))
We should eliminate the point where x=0 as it does not fulfill the condition of the problem ( the width should be greater than 0)
Hence, the width and height of the rectangle for which the perimeter of the window will be as small as possible are (3sqrt(2), 2sqrt(2)).
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A cylindrical cooler ha a diameter of 30 inche and a height of 24 inche. Runner in
a marathon can ue cone haped cup to get a drink from the cooler. If the cup have a
diameter of 3 inche and a height of 4 inche, how many full cup would be able to
be filled from the cooler?
So, 600 full cup would be able to be filled from the cooler. This can be solved using the concept of volume of cylinder.
What is volume of cylinder?The three-dimensional form of a cylinder is made up of two parallel circular bases connected by a curving surface. The right cylinder is created when the centers of the circular bases cross each other. The measure of space within a cylinder is measured by its volume. Find it by dividing the base area by the height. V = πr²h is the formula for the volume of a cylinder with base radius "r" and height "h."
Given that,
diameter of cylinder = 30 inch
diameter of cup = 3 inch
height of cylinder = 24 inch
height of cup = 4 inch
Calculate the volume of the cylinder:
Volume = πr²h
putting the values we get:
Volume = (3.14)(30/2)²(24)
Volume = (3.14)(15)²(24)
Volume = (3.14)(225)(24)
Volume = 16959 in³
Calculate the volume of the cup:
Volume = (3.14)(3/2)²(4)
Volume = (3.14)(1.5)²(4)
Volume = (3.14)(2.25)(4)
Result
Volume = 28.26 in³
Divide the volume of the cylinder by the volume of the cup, we get:
Number of full cups = 16959 in³ / 28.26 in³
Number of full cups = 600
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13. Solve for x. (show work)
Answer:
The value of x is 12.
i think it is correct.
Theater tickets sold for $7.50 on
the main floor and $, in the
balcony. The total revenue was
$3250, and there were 100 more
main-floor tickets sold than
balcony tickets. Find the number
of each type of ticket sold.
(in Substitution method)
Cant figure the work out :/
Joe painted 3/4 of a bedroom in 1/2 of a day. How many days will it take for Joe to paint one bedroom?
Answer:
3/4
Step-by-step explanation:
Answer:
2/3 of a day
Step-by-step explanation:
3/4 : 1/2 = 1 : X
X=2/3
Find the value of x and y so that the quadrilateral is a parallelogram.
(4x - 35° (y + 15)
(2y-5) (3x + 10)
X=
y =
Therefore, for x = 45 and y = 20, the quadrilateral is a parallelogram.
Define quadrilateral.In geometry a quadrilateral is a four-sided polygon, having four edges and four corners.
What is a polygon?A polygon is a closed polygonal chain made up of a limited number of straight-line segments and is a type of planar figure in geometry. A polygon is an area that is bordered by a bounding circuit, a bounding plane, or both.
We know opposite sides of a parallelogram are equal in length and parallel. Given opposite sides of a parallelogram are:
(4x - 35) and (3x + 10)
(y + 15) and (2y - 5)
Now, setting those opposite sides equal to each other:
4x - 35 = 3x + 10 = >x = 45
y + 15 = 2y - 5 => y = 20
Therefore, x = 45 and y = 20, the quadrilateral is a parallelogram.
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In the adjoining figure, the area of the rectangular surfaces of the prism is 720 sq. Cm, XX' 20 cm and XY : XZ: YZ = 5:3 : 4, find the length of XY
The length of XY, with the area of the rectangular surface of the prism 720 sq.cm, XX' 20 cm and XY : XZ: YZ = 5:3:4, is 12 cm.
Area of the rectangular surface of the prism = 720 sq. cm
XX' = 20 cm
XY : XZ: YZ = 5:3:4
As we know, area of prism = 3 × area of rectangle
⇒720 = 3 × area of rectangle
⇒area of rectangle = 720/3
⇒XY × XX' = 240
⇒XY × 20 = 240
⇒XY = 240/20
⇒XY = 12 cm
Thus, the length of the XY is 12 cm.
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Write an equation in slope-intercept form for each line at the right. Line one goes from (-6,7) to (1,-7) and line two goes from about (1.25,7) to (3.25,-7)
y=-2x-5 and y=-7x+15.75 are equations in slope-intercept form for each line.
What is slope intercept form of line?The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
We need to find equation in slope-intercept form of line passing through of (-6,7) to (1,-7) and one more line passing through (1.25,7) to (3.25,-7)
Slope of line with (-6,7) to (1,-7) is m=-7-7/1+6=-14/7
=-2
y intercept we have to find
7=-2(-6)+b
7=12+b
-5=b
So slope intercept form of line passing through (-6,7) to (1,-7) is y=-2x-5
Now Slope of line with (1.25,7) to (3.25,-7) is
m=-7-7/3.25-1.25
m=-14/2=-7
y intercept we have to find
7=-7(1.25)+b
7=-8.75+b
b=15.75
So slope intercept form of line passing through (1.25,7) to (3.25,-7) is y=-7x+15.75
Hence, y=-2x-5 and y=-7x+15.75 are equations in slope-intercept form for each line.
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Conan borrows $3,000 at a yearly simple interest rate of 1.6% for 2 years find out how much he owes and interest and how much he needs to pay back
Answer:
P=3000$
T=2 years
R=1.6% per annum
Now,
interest=(3000×2×1.6)/100=96$
Amount=P+interest=3096$
Hence,Conan needs to pay back 3096$ and the interest is 96$
An item on ale cot 20% of the original price if the original price wa $95 what i the ale price
By using formula and solving we get the item is on sale for $76.
What is selling price?
The selling price is the amount of money that a seller asks for in exchange for a product or service. It is also known as the "list price" or "retail price" and it is the price at which an item is intended to be sold. Selling price is usually set by the manufacturer or the retailer, taking into account the cost of production, distribution, and marketing, as well as competition and market demand. The selling price is usually higher than the cost of production, which includes the cost of the materials, labor, and overhead expenses.
What is the formula to calculate selling price?The formula to calculate the selling price of a product or service depends on the information available and the desired level of accuracy. However, there are a few common formulas used to calculate the selling price based on different factors.
Cost-plus pricing formula: This formula calculates the selling price by adding a markup percentage to the cost of the product or service.
The formula is: Selling price = Cost + (Cost x Markup percentage)
If the original price of an item was $95 and it is now on sale for 20% off, we can calculate the sale price using the following formula:
Sale price = Original price x (1 - Discount percentage)
In this case, the discount percentage is 20%, so we can express it as 0.2. Therefore, the formula becomes:
Sale price = $95 x (1 - 0.2)
To calculate the sale price, we need to multiply the original price by (1 - 0.2) which is (1-0.2) = 0.8
Sale price = $95 x 0.8
Sale price = $76
So, the item is on sale for $76.
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Question 17
Galle bought a purse for $22.50. Gale's thend Brenda saw the purse and said she would give Gale $35 if Gale would sell her the new purse right then.
mely how much profit as a percent did Gale make from selling the purse to Brenda?
A.35.7%
B.55.6%
C.64.3%
D.155.6%
So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%
What is profit and loss?Profit and Loss is a financial statement that shows a company's revenue, costs, and expenses over a certain period of time, such as a month or a year. The purpose of a P&L statement is to show the company's financial performance and to determine whether the company is making a profit or incurring a loss.
What is Profit Percentage?The proportion that the retailer makes after selling a good at a price greater than its cost is the product's profit margin. P% indicates it.
Profit Percentage P% = {(selling price – cost price) / cost price} x 100.
The selling price of the purse is $35 and the original cost of the purse is $22.50. So the profit is $35 - $22.50 = $12.50
Profit as a percent = (Profit / Original cost) * 100
Profit as a percent = ($12.50 / $22.50) * 100 = 55.6%
So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%
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Pierre, the mountain climbing ant, moves along the x-axis so that at
time t its position is given by x(t) = 2cos(π/2 t^2).
For values of t in the interval [-1,1]
(a)Find an expression for the velocity of the ant at any given time t.
(b) Find an expression for the acceleration at any given time t.
(c)Determine the values of t for which the ant is moving to the right.
Justify your answer.
(d) Determine the values of t for which the ant changes direction.
Justify your answers
The velocity of an ant moving along the x-axis whose position is given by x(t) = 2cos(π/2 t^2) is v(t) = -πtsin(π/2 t^2) and acceleration is a(t) = -π²t²cos(π/2 t^2) - πtsin(π/2 t^2). The ant moves in right direction in the time interval [-1, 0) and changes direction at t = 0.
(a) To find the velocity of the ant at any given time t, we need to take the derivative of the position function x(t) with respect to t. The derivative of x(t) = 2cos(π/2 t^2) is:
v(t) = -πtsin(π/2 t^2)
So the velocity of the ant at time t is given by -2πsin(π/2 t^2)
(b) To find the acceleration at any given time t, we need to take the derivative of the velocity function v(t) with respect to t. The derivative of v(t) = -πtsin(π/2 t^2) is:
a(t) = -π²t²cos(π/2 t^2) - πtsin(π/2 t^2)
So the acceleration of the ant at time t is given by -π²t²cos(π/2 t^2) - πtsin(π/2 t^2).
(c) To determine the values of t for which the ant is moving to the right, we need to look at the sign of the velocity function v(t) = -πtsin(π/2 t^2). Since the sine function oscillates between -1 and 1, this function will be positive when sin(π/2 t^2) is negative, and negative when sin(π/2 t^2) is positive. Moving rights means positive value of x.
Therefore, the ant is moving to the right when sin(π/2 t^2) < 0. That is
(π/2)t^2 < sin⁻¹(0)
sin⁻¹(0) = nπ, where n = ..., -2, -1, 0, 1, 2, ...
t is in interval [-1, 1] so π/2t^2 is in interval [0, π/2]
sin⁻¹(0) = 0
(π/2)t^2 < 0
Therefore t < 0
That is possible values of t is [-1, 0)
(d) To determine the values of t for which the ant changes direction, we need to look at the sign of the acceleration function a(t) = -π²t²cos(π/2 t^2) - πtsin(π/2 t^2).
When ant change direction a(t) = 0.
-π²t²cos(π/2 t^2) - πtsin(π/2 t^2) = 0
πtcos(π/2 t^2) + sin(π/2 t^2) = 0
sin(π/2 t^2) = -πtcos(π/2 t^2)
tan(π/2 t^2) = -πt
On solving possible values of t in the interval [-1, 1] is 0.
So, the ant changes direction when t = 0.
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(01.03 MC)
The Kelly school district gives awards to its schools based on overall student attendance. The data for attendance are shown in the table below, where Min represents the fewest days attended and Max represents the most days attended for a single student:
School
Min
Max
Range
Mean
Median
IQR
σ
High School M
128
180
52
141
160
55.5
41.5
High School N
131
180
49
159
154
48.5
36.5
High School P
140
180
40
153
165
32.5
31.5
Part A: If the school district wants to award the school that has the most consistent attendance among its students, which high school should it choose and why? Justify your answer mathematically. (5 points)
Part B: If the school district wants to award the school with the highest average attendance, which school should it choose and why? Justify your answer mathematically. (5 points) (10 points)
Answer:
a: School W is has the most consistent attendance
b: School W has the highest average attendance
Step-by-step explanation:
For a:
The most consistent school will be the school whose data has the smallest variance. *Consistent doesn't mean the best, it's just the least differing among it's own data. The variance tells us how spread out the data is, so the school with the smallest variance is the most consistent.
See photo 1 for the calculations of the variances of each school...
For b:
Take the mean for each school. Whichever has a higher value is the school with the highest average.
See photo 1 for the calculations if the means for each school. (the mean is used to calculate variance, so we will do this part first)
What is the area of this parallelogram?
Answer: B
Step-by-step explanation:
Area = 4 x 5
= 20 cm^2
Remember that area of parallelogram is the base x perpendicular height. is The perpendicular height is not 6cm but 5cm. (right angle labelled on diagram)
Answer: 20 cm²
Step-by-step explanation:
area parallelogram = base x height
=> 4 x 5 = 20
A particle traveled a distance of 9. 0 x 1012 meters at a rate of 1. 8 x 105 meters
per second. If distance = rate x time, how many seconds did it take the particle to
travel the specified distance?
A particle takes 5 × 10^7 sec of time to travel a distance of 9.0 × 10^12 meters at a rate of 1.8 × 10^5 meters.
What is speed?
Speed indicates how quickly something or someone is moving. If one knows how far something has travelled and how long it took to get there, then one can calculate its average speed.
The particle travels at a rate of 1.8 × 10^5 m.
The particle travels a distance of 9.0 × 10^12 m.
Let the time taken for the particle to travel be x.
The formula for calculating the distance traveled by the particle is -
distance = rate × time
time = distance/rate
Plugging in the values in the equation -
x = 9.0 × 10^12/1.8 × 10^5
x = 9.0/1.8 × (10^12-5)
x = 5 × 10^7 sec
Therefore, the time taken by the particle to travel is 5 × 10^7 sec.
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How do you find the slope of a line example?
The easiest way to find the slope of a line is converting the line equation into the slope-intercept form.
There are 3 forms of line equations:
- slope intercept form, the equation is given by:
y = mx + b
Where:
m = slope
- point slope form, the equation is given by:
y − y₁ = m (x - x₁)
Where:
m = slope
- standard form: Ax + By = C
The easiest way to find the slope of a line is to convert it into a slope-intercept form.
Example:
Line equation in standard form:
2x + 4y = 6
We will convert it into slope-intercept form.
4y = -2x + 6
y = (-2/4) x + 6
y = (-1/2) x + 6
Hence, the slope is (-1/2)
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