Question

kira and lyra race at track practice. the equation and the graph each represent the runner’s distance from the start in yards, y, as a function of time in seconds, x
kira: y = 5x
what is kira’s speed? find the rate of change.
kira’s speed = 5 yards per second
what is lyra’s speed? find the rate of change.
lyra’s speed = \boxed{} yards per second
graph of lyras distance vs time: y-axis (distance (yd)) from 0 to 80, x-axis (time (s)) from 0 to 8+; line through (0,0) and increasing

Explanation:

Step1: Identify two points on Lyra's graph

From the graph, when \(x = 2\) (seconds), \(y=20\) (yards); when \(x = 4\) (seconds), \(y = 40\) (yards).

Step2: Calculate the rate of change (speed)

The formula for the rate of change (slope) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substitute \((x_1,y_1)=(2,20)\) and \((x_2,y_2)=(4,40)\) into the formula:
\(m=\frac{40 - 20}{4 - 2}=\frac{20}{2}=10\)

Answer:

\(10\) yards per second