Question

question
dylans 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, what quiz score should someone who studied 5.5 hours expect?

Explanation:

Step1: Find the slope of the line

Use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\) with points \((3.5,77)\) and \((4,80)\).
\(m=\frac{80 - 77}{4 - 3.5}=\frac{3}{0.5}=6\)

Step2: Find the equation of the line

Use the point - slope form \(y - y_1=m(x - x_1)\). Using point \((3.5,77)\) and \(m = 6\):
\(y-77=6(x - 3.5)\)
\(y-77=6x-21\)
\(y=6x + 56\)

Step3: Substitute \(x = 5.5\) into the equation

\(y=6\times5.5+56\)
\(y = 33+56\)
\(y=89\)

Answer:

\(89\)