Question

A bunny hop is a bike trick in which the rider brings both tires off the ground without using a ramp. The table shows the height y (in inches) of a bunny hop on a bike that weighs x pounds.

part b.
Write a linear function that relates the height of a bunny hop to the weight of the bike.

y=

Answer 1

All linear functions are in the form y = mx + b, where m is the slope and b is the y-intercept (where the function crosses the y-axis when graphed).

The given points are:
(19, 10.2), (21, 9.8), (23, 9.4)

To find the slope m of the graph, pick two points, then use the slope formula $m = \frac{(y2-y1)}{(x2-x1)}$, where the two points are (x1, y1) and (x2, y2).
Let's use the first two points (19, 10.2) and (21, 9.8)
$m = \frac{9.8-10.2}{21-19} = -0.2$

Now that we know the slope m = -0.2, we can find the y-intercept b by substituting the slope and one of the points into y = mx + b.
Let's use the point (19, 10.2)
y = mx + b
(10.2) = (-0.2)(19) + b
10.2 = -3.8 + b
b = 14

Now that we know the y-intercept b = 14 and the slope m = -0.2, we can substitute these values into y = mx + b write the equation of the line.
y = mx + b
y = -0.2x + 14