Peter works as a delivery person for a bike shipping company. The graph shows a linear model for his
delivery times on different days.

(a) what is the equation of the line, first written in point-slope form and then written in slope- intercept form? show how you determined the equation.

(b) based on the linear model, predict how long it initially took peter to deliver his packages (y-intercept) approximately how much did his delivery time decrease per day (slope)? Complete sentences

Answer/Step-by-step explanation:

a. Using a point on the graph, (6, 12), and the slope of the line, we can first generate an equation in the point-slope form, given as [tex] y - b = m(x - a) [/tex], where,

m = slope, and (a, b) is a point on the line.

Using two points, (6, 12) and (3, 21), let's find slope, m.

[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{21 - 12}{3 - 6} = \frac{9}{-3} = -3 [/tex]

Using a point (6, 12) and slope, m = -3, generate an equation in the point-slope form by substituting a = 6, b = 12, and m = -3 in [tex] y - b = m(x - a) [/tex].

✅Equation in point-slope form would be:

[tex] y - 12 = -3(x - 6) [/tex]

Rewrite this to make it be in the slope-intercept form, [tex] y = mx + b [/tex].

[tex] y - 12 = -3(x - 6) [/tex]

[tex] y - 12 = -3x + 18 [/tex]

Add 12 to both sides

[tex] y = -3x + 18 + 12 [/tex]

[tex] y = -3x + 30 [/tex]

✅The equation in slope-intercept form is [tex] y = -3x + 30 [/tex]

b. ✍️Based on the linear model, [tex] y = -3x + 30 [/tex], the 30 represents b = y-intercept.

✅Therefore, it took Peter 30 mins long initially to deliver his package.

✍️Based on the linear model, [tex] y = -3x + 30 [/tex], "-3" represents the slope.

✅Therefore,  Peter's delivery time decreased 3 mins per day.

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Revelation 22:12
“Behold, I am coming soon, bringing my recompense with me, to repay everyone for what he has done.

1 John 2:18
Children, it is the last hour, and as you have heard that antichrist is coming, so now many antichrists have come. Therefore we know that it is the last hour.

AGAIN, PLEASE EXCEPT JESUS AS YOUR ONE AND ONLY SAVIOR!!!
FOR TIME IS TOO SHORT, THE SECOND COMING OF THE LORD IS VERY SOON!!
PLEASE REPENT OF YOUR SINS, ASK GOD FOR FORGIVENESS!!!!

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