Question

speed of pitch vs. number of hits
the graph above shows a line of best fit for the data collected at a batting cage for the number of hits in relation to the speed of the pitch. what is the equation of the line of best fit?
a. $y = -0.75x + 98.75$
b. $y = -0.25x + 96.25$
c. $y = -0.75x + 96.25$
d. $y = -0.25x + 98.75$

Explanation:

Step1: Identify two points on the line

From the graph, when \( x = 0 \), \( y \approx 98.75 \) (y-intercept). Another point: when \( x = 100 \), \( y \approx 23 \) (approximate from the line).

Step2: Calculate the slope (\( m \))

Slope formula: \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Using \( (0, 98.75) \) and \( (100, 23) \):
\( m=\frac{23 - 98.75}{100 - 0}=\frac{-75.75}{100}\approx - 0.75 \) (close to -0.75).

Step3: Check the y-intercept and slope in options

The slope is approximately -0.75, and y-intercept is ~98.75. Option A has \( m = - 0.75 \) and \( b = 98.75 \), matching the calculations.

Answer:

A. \( y = -0.75x + 98.75 \)