Question

The graph shows the relationship between the weight of a box and the number of books added to the box.

A graph shows number of books labeled 1 to 10 on the horizontal axis and weight of box (pounds) on the vertical axis. A line increases from 1 to 6.

What function represents the weight of a box based on x, the number of books?

f(x) = 0.5x + 1.5
f(x) = 0.75x + 2
f(x) = 1.5x + 0.5
f(x) = 2x + 0.75

Answer 1

Pick two points on the line, e.g. (1, 2) and (6, 4.5). Slope = (4.5 − 2)/(6 − 1) = 2.5/5 = 0.5.
Use (1,2): 2 = 0.5(1) + b → b = 1.5.
So f(x) = 0.5x + 1.5.