Question

lukes 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 83?

Explanation:

Step1: Find two points on the line of best - fit

We can take two points, say $(0, 50)$ and $(3.5, 77)$.

Step2: Calculate the slope of the line

The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{77 - 50}{3.5-0}=\frac{27}{3.5}=\frac{54}{7}\approx7.71$.

Step3: Find the equation of the line in slope - intercept form $y = mx + b$

Using the point $(0, 50)$, we know that $b = 50$. So the equation of the line is $y=\frac{54}{7}x + 50$.

Step4: Solve for $x$ when $y = 83$

Set $y = 83$ in the equation $83=\frac{54}{7}x+50$.
Subtract 50 from both sides: $83 - 50=\frac{54}{7}x$, so $33=\frac{54}{7}x$.
Multiply both sides by $\frac{7}{54}$: $x=\frac{33\times7}{54}=\frac{231}{54}=\frac{77}{18}\approx4.28$.

Answer:

Approximately 4.28 hours