Scott works as a delivery person for a 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 from? 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) ? please help me with this please

a) In order to use the point-slope form of the equation for a line, we need to know the slope of the line. (We need that anyway for the remaining parts of the question.) The slope can be found by looking at the graph, or by calculating from the coordinates of the points marked on the graph.

For each unit the line goes in the horizontal direction, it drops 3 units in the vertical direction. This is confirmed by the fact that the marked points are 3 units (days) apart horizontally, and 9 units (minutes) apart vertically, with the one on the right being lower (more negative). That is, the slope is -3/1 = -3.

Using the point (3, 21), the point-slope equation is ...

... y -21 = -3(x -3)

Solving for y and simplifying, the slope-intercept equation is

... y = -3x +9 +21 . . . . eliminate parentheses, add 21

... y = -3x + 30

b) The intercept in the above equation is 30, meaning after 0 days on the job, delivery took 30 minutes.

The slope is -3, meaning it took 3 minutes less each day. The decrease was 3 minutes per day.