nolans math teacher plots student grades on their weekly quizzes against the number of hours they say they…
nolans 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 4.5 hours expect?
Answer
Answer:
92
Explanation:
Step1: Find the slope of the line
The line passes through points $(3.5,84)$ and $(4,88)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{88 - 84}{4 - 3.5}=\frac{4}{0.5}=8$.
Step2: Find the y - intercept of the line
Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(3.5,84)$ and $m = 8$. We have $y-84=8(x - 3.5)$. Expanding gives $y-84=8x-28$, so $y = 8x+56$.
Step3: Predict the score for 4.5 hours
Substitute $x = 4.5$ into $y = 8x+56$. Then $y=8\times4.5+56=36 + 56=92$.