Identifying the Graph of an Inequality
Which is the graph of 4x + 2y < 3?
y
4
TY
NA
2
2
2
21
x
41
2
4
-4-2
2.
4
-4
2.
4
2
4
-2
-2
x

Answer:

The point-slope form of the equation of a line is ...

 y -h = m(x -k)

for a line with slope m through point (h, k).

Comparing this to the given equation, you see that ...

 h = -2, m = 1, k = -4

The line has a slope of 1 and goes through the point (-4, -2). This information is useful for graphing.

__

You can also rearrange the equation to slope-intercept form by subtracting 2 from both sides.

 y = x +2

This has a slope of 1 and crosses the y-axis at y=2. It graphs the same as the above.

The graph of 4x + 2y < 3 is the region below the line 4x + 2y = 3.

The graph is given below.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal =

Greater than and equal=

We have,

The graph of 4x + 2y < 3 is the region in the coordinate plane that satisfies the inequality.

To graph this inequality, we can start by graphing the line 4x + 2y = 3.

This line has a slope of -2 (because it can be written in the form

y = (-2x/1) + (3/2)), and a y-intercept of (0, 3/2).

We can plot this point on the y-axis and use the slope to find other points on the line.

For example, if we move one unit to the right from the y-intercept, we will move down two units (since the slope is -2), giving us the point (1, 1/2). Similarly, if we move one unit to the left from the y-intercept, we will move up two units, giving us the point (-1, 5/2).

We can connect these points to graph the line.

Therefore,

The graph of 4x + 2y < 3 is the region below the line 4x + 2y = 3.

Learn more about inequalities here:

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