Question

question 12
the scatter plot below shows the relationship between the number of hours students studied and their scores
on a math quiz.
study hours vs. quiz scores
which function, f(h), best approximates a students quiz score, f, as a function of the number of hours studied,
h?
a. f(h)=h + 32
b. f(h)=4.5h + 52
c. f(h)=2h + 75
d. f(h)=5h + 20

Explanation:

Step1: Estimate the slope

Pick two points from the scatter - plot. Let's assume when \(h = 0\), \(f(h)\approx20\) (the \(y\) - intercept). When \(h = 10\), \(f(h)\approx70\).
The slope \(m=\frac{\Delta y}{\Delta h}=\frac{70 - 20}{10-0}=\frac{50}{10}=5\)

Step2: Use the slope - intercept form \(y = mx + b\)

The slope - intercept form of a linear function is \(f(h)=mh + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.
We found \(m = 5\) and \(b\approx20\)

Answer:

D. \(f(h)=5h + 20\)