Question

Brian sat in a massage chair at a shopping mall for 8 minutes and paid $9. Norah sat in

the same massage chair for 12 minutes and paid $11. If the relationship between the
number of minutes and the amount paid is linear, with x representing the minutes and y
representing the amount paid in dollars, which of these equations models the situation?
A. x = 0.5y + 5
B. x = y + 1
C. y = 0.5x + 5
D. y = x + 1

Answer 1

(1/2)x + $5 (Answer A)

Explanation:

Two points on the line representing the cost are (8, $9) and (12, $11).

The change in x is 4 (minutes); this is the 'run.' The change in y is $2 (this is the 'rise'). Thus, the slope of this line is m = rise / run = $2/(4 min), or 1/2 dollar per min.

Applying the slope-intercept formula y = mx + b, we get:

$9 = (1/2)(8) + b, and from this we see that b must be $5.

Then the correct equation is y = (1/2)x + $5.