Question

the scatter plot shows the time spent studying, x, and the quiz score, y, for each of 25 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 = \square (b) using your equation from part (a), predict the quiz score for a student who spent 60 minutes studying. round your prediction to the nearest hundredth.

Explanation:

Step1: Pick two points on trend line

Choose points (10, 25) and (80, 95) (approximate from scatter plot)

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{95-25}{80-10}=\frac{70}{70}=1.00$

Step3: Find y-intercept $b$

Use $y=mx+b$ with (10,25):
$25=1.00\times10 + b$
$b=25-10=15.00$

Step4: Write line of best fit

$y=1.00x + 15.00$

Step5: Predict score for $x=60$

Substitute $x=60$ into the equation:
$y=1.00\times60 + 15.00=75.00$

Answer:

(a) $y = 1.00x + 15.00$
(b) $75.00$