Question

the scatter plot shows the number of hours worked, $x$, and the amount of money spent on entertainment, $y$, by 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.)
scratch area (not part of answer)
(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 money spent on entertainment for a student who works 8 hours. round your prediction to the nearest hundredth.
$\square$

Explanation:

Step1: Identify two points on trend line

Choose points like $(4, 8)$ and $(20, 22)$ (approximate from plot)

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{22-8}{20-4}=\frac{14}{16}=0.875\approx0.88$

Step3: Find y-intercept $b$

Use $y=mx+b$ with $(4,8)$:
$8 = 0.88(4)+b$
$8=3.52+b$
$b=8-3.52=4.48$

Step4: Write line of best fit

Combine slope and intercept: $y=0.88x+4.48$

Step5: Predict for $x=8$

Substitute $x=8$ into the equation:
$y=0.88(8)+4.48$
$y=7.04+4.48=11.52$

Answer:

(a) $y = 0.88x + 4.48$
(b) $\$11.52$