Question

the scatter plot shows the number of hours worked, x, and the amount of money spent on entertainment, y, by each of 24 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 money spent on entertainment for a student who works 8 hours. round your prediction to the nearest hundredth. $\square

Explanation:

Step1: Find two points on the line

Looking at the scatter plot, we can approximate two points on the line of best fit. Let's take (4, 9) and (20, 24) as approximate points.

Step2: Calculate the slope (m)

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the points \((x_1,y_1)=(4,9)\) and \((x_2,y_2)=(20,24)\), we get \( m=\frac{24 - 9}{20 - 4}=\frac{15}{16}\approx0.94 \).

Step3: Find the y - intercept (b)

Using the point - slope form \( y - y_1=m(x - x_1) \) with \((x_1,y_1)=(4,9)\) and \( m = 0.94 \).
\( y-9 = 0.94(x - 4) \)
\( y-9=0.94x-3.76 \)
\( y=0.94x + 9 - 3.76 \)
\( y=0.94x+5.24 \) (approximate equation of the line of best fit)

Step4: Predict for x = 8

Substitute \( x = 8 \) into the equation \( y = 0.94x+5.24 \).
\( y=0.94\times8 + 5.24 \)
\( y = 7.52+5.24 \)
\( y=12.76 \)

Part (a)

Answer:

\( y = 0.94x + 5.24 \) (answers may vary slightly depending on the points chosen for approximation)

Part (b)