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.)
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 10 hours. round your prediction to the nearest hundredth.
( $ square )

Explanation:

Step1: Find two points on the line of best fit

Let's assume two points \((x_1,y_1)=(4,12)\) and \((x_2,y_2)=(20,24)\)

Step2: Calculate the slope \(m\)

The formula for slope is \(m=\frac{y_2 - y_1}{x_2 - x_1}\)

$$m=\frac{24 - 12}{20 - 4}=\frac{12}{16}=0.75$$

Step3: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((4,12)\) and \(m = 0.75\)

$$y-12=0.75(x - 4)$$

$$y-12=0.75x-3$$

$$y=0.75x + 9$$

Step4: Predict for \(x = 10\)

Substitute \(x = 10\) into \(y=0.75x + 9\)

$$y=0.75\times10+9$$

$$y=7.5+9$$

$$y = 16.5$$

Answer:

(a) \(y = 0.75x+9\)
(b) \(16.50\)