Question

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

Questions are on the next page.
⦁ Graph is on the previous page

⦁ Identify two points on the line and write the coordinate pairs below.

⦁ Use your two points to find the slope, and make sure to show your work.

⦁ Use your slope from Part B and find the equation of the line in point-slope form. Show your work and work through the steps to transform the equation from point-slope form into slope-intercept form.

⦁ Based on the equation you found in Part C, predict how long it initially took Scott to deliver his packages. Approximately how much did his delivery time decrease per day?

Answer 1

• (3, 21), (6, 12)
• -3
• y -21 = -3(x -3) ⇒ y = -3x +30
• 30 minutes; 3 minutes

Explanation:

a) The two marked points have coordinates (days, minutes) = (3, 21) and (6, 12).

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b) The slope is the vertical change (rise) divided by the horizontal change (run). For these two points, that is ...

rise/run = (12-21)/(6-3) = -9/3 = -3 = slope

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c) The point-slope form of the equation for a line is ...

y -k = m(x -h) . . . . . . for slope m through point (h, k)

Using the first point and the slope we found, this is ...

y -21 = -3(x -3) . . . . . point-slope form

Add 21 and eliminate parentheses:

y = -3x +9 +21

y = -3x +30 . . . . . . . . collect terms; slope-intercept form

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d) The initial time is the time corresponding to day 0, the value of y when x=0. It is 30 minutes.

The slope in part (b) tells us the time decreases by 3 minutes per day.