carloss math teacher plots student grades on their weekly quizzes against the number of hours they say they…

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?

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?

Answer

Explanation:

Step1: Find the slope of the line

Use two - points on the line, say $(1,62)$ and $(4,80)$. The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m=\frac{80 - 62}{4 - 1}=\frac{18}{3}=6$.

Step2: Find the y - intercept of the line

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(1,62)$ and $m = 6$. So $y-62=6(x - 1)$, which simplifies to $y=6x+56$.

Step3: Solve for x when y = 89

Set $y = 89$ in the equation $y=6x + 56$. Then $89=6x+56$. Subtract 56 from both sides: $89 - 56=6x$, so $33 = 6x$. Divide both sides by 6: $x=\frac{33}{6}=5.5$.

Answer:

5.5