Question

a scatter - plot shows the time spent studying, x, and the quiz score, y, for each of 24 students. use the scatter - plot to answer the parts below. (note that you use the graphing tools to help you approximate the line.) (a) write an approximate equation of the line of best fit. round the coefficients to the nearest hundredth. y = (b) using your equation from part (a), predict the quiz score for a student who spent 40 minutes studying. round your prediction to the nearest hundredth.

Explanation:

Step1: Select two points on line

Let's assume two points on the line of best - fit as $(x_1,y_1)$ and $(x_2,y_2)$ by observing the scatter - plot. Suppose we pick $(x_1 = 10,y_1=30)$ and $(x_2 = 30,y_2 = 70)$.

Step2: Calculate the slope

The slope $m$ of the line is given by the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values, we have $m=\frac{70 - 30}{30 - 10}=\frac{40}{20}=2$.

Step3: Find the y - intercept

We use the point - slope form $y - y_1=m(x - x_1)$ and then convert it to the slope - intercept form $y=mx + b$. Using the point $(x_1 = 10,y_1 = 30)$ and $m = 2$, we get $y-30=2(x - 10)$. Expanding, $y-30=2x-20$. Then $y=2x + 10$.

Step4: Predict the score

For part (b), when $x = 40$, we substitute $x = 40$ into the equation $y=2x + 10$. So $y=2\times40+10=80 + 10=90$.

Answer:

(a) $y = 2x+10$
(b) $90$