Question

the scatter plot shows the time spent studying, x, and the quiz score, y, for each of 23 students. use the scatter plot to answer the parts below. (note that you can 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 50 minutes studying. round your prediction to the nearest hundredth.

Explanation:

Step1: Estimate two points on the line

Let's assume two points on the line of best - fit from the scatter - plot. Suppose the points are $(20,40)$ and $(60,80)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points $(x_1,y_1)=(20,40)$ and $(x_2,y_2)=(60,80)$ gives $m=\frac{80 - 40}{60 - 20}=\frac{40}{40}=1$.

Step3: Calculate the y - intercept $b$

Using the point - slope form $y - y_1=m(x - x_1)$ and the point $(20,40)$ with $m = 1$, we have $y-40=1\times(x - 20)$. Simplifying to the slope - intercept form $y=mx + b$ gives $y=x+20$.

Step4: Predict the quiz score for $x = 50$

Substitute $x = 50$ into the equation $y=x + 20$. So $y=50+20=70$.

Answer:

(a) $y=x + 20$
(b) $70.00$