Question

carloss math teacher plots student grades on their weekly quizzes against the number of hours they say they study on the pair of coordinate axes and then draws the line of best fit. based on the line of best fit, how much time should someone study to expect a quiz score of 89?

Explanation:

Step1: Find line slope

Use points $(3.5,77)$ and $(4,80)$
Slope $m = \frac{80-77}{4-3.5} = \frac{3}{0.5} = 6$

Step2: Get line equation

Use point-slope form with $(4,80)$
$y - 80 = 6(x - 4)$
Simplify: $y = 6x -24 +80 = 6x +56$

Step3: Solve for $x$ when $y=89$

Substitute $y=89$ into equation:
$89 = 6x +56$
$6x = 89 -56 = 33$
$x = \frac{33}{6} = 5.5$

Answer:

5.5 hours