the scatter plot shows the number of hours worked, x, and the amount of money spent on entertainment, y, by…

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

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

Answer

Answer:

(a) $y = 0.65x+ 6.00$ (b) $11.20$

Explanation:

Step1: Select two points on the line of best - fit

Let's choose two points approximately on the line. Say $(4,8.6)$ and $(20,19)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{19 - 8.6}{20 - 4}=\frac{10.4}{16}=0.65$.

Step3: Find the y - intercept $b$

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(4,8.6)$ and $m = 0.65$. $y-8.6 = 0.65(x - 4)$ $y-8.6=0.65x-2.6$ $y=0.65x + 6.00$

Step4: Predict for $x = 8$

Substitute $x = 8$ into the equation $y=0.65x + 6.00$. $y=0.65\times8+6.00$ $y = 5.2+6.00$ $y = 11.20$