dylans math teacher plots student grades on their weekly quizzes against the number of hours they say they…
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?
Answer
Explanation:
Step1: Find the slope of the line
The line passes through points $(3.5,77)$ and $(4,80)$. The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m=\frac{80 - 77}{4 - 3.5}=\frac{3}{0.5}=6$.
Step2: Find the y - intercept
Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(3.5,77)$ and $m = 6$. Then $y-77=6(x - 3.5)$. Expand to get $y-77=6x-21$. Solve for $y$: $y=6x + 56$.
Step3: Predict the score for 5.5 hours
Substitute $x = 5.5$ into $y=6x + 56$. So $y=6\times5.5+56=33 + 56=89$.
Answer:
89