Question

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 1

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 $y - b = m(x - a)$, 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.

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{21 - 12}{3 - 6} = \frac{9}{-3} = -3$

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 $y - b = m(x - a)$.

✅Equation in point-slope form would be:

$y - 12 = -3(x - 6)$

Rewrite this to make it be in the slope-intercept form, $y = mx + b$.

$y - 12 = -3(x - 6)$

$y - 12 = -3x + 18$

Add 12 to both sides

$y = -3x + 18 + 12$

$y = -3x + 30$

✅The equation in slope-intercept form is $y = -3x + 30$

b. ✍️Based on the linear model, $y = -3x + 30$, the 30 represents b = y-intercept.

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

✍️Based on the linear model, $y = -3x + 30$, "-3" represents the slope.

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