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





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 Scott to deliver his packages (y-intercept). Approximately how much did his delivery time decrease per day (slope)?

 Oct 23, 2018

well they've highlighted two points on this line so I guess they want you to use them.


\(\text{the two points are }(3,21) \text{ and }(6,12) \\ \text{we calculate the slope as }m = \dfrac{y_2-y_1}{x_2-x_1} \\ m = \dfrac{12 - 21}{6-3} = \dfrac{-9}{3}=-3 \\ \text{using the first point, point slope form is thus}\\ (y-21)=-3(x-3) \\ \text{and with a bit of rearranging we get }\\ y = -3x + 30 \text{ which is slope intercept form}\)


for (b) just plug in x=0 for the y intercept


we already found the slope as m=-3


so his delivery time decreased 3 minutes per day

 Oct 23, 2018

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