Question

Mel works as a delivery person for Amazon. 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 Phillip to deliver his packages.
Approximately how much did his delivery time decrease per day?

Answer 1

Explanation:

Equation of a line passing through (h, k) in point slope form is given by,

y - k = m(x - h)

From the graph attached,

Slope of the line passing through (6, 12) and (3, 21),

m =
`(y_2-y_1)/(x_2-x_1)`

=
`(21-12)/(3-6)`

= -3

Therefore, point - slope form of the line passing through (3, 21) will be,

y - 21 = -3(x - 3)

Now convert this equation in slope intercept form,

y = -3x + 9 + 21

y = -3x + 31

(b). For x = 1 Or day 1

y = -3(1) + 31

y = 28 minutes

Therefore, Phillip took 28 minutes initially to deliver his packages.

Slope of the line states the decrease in the delivery time per day that is 3 minutes per day.