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 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 = (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 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 = (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

Explanation:

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

Let's assume two points on the line of best - fit from the scatter - plot. Suppose the points are $(x_1,y_1)=(4,12)$ and $(x_2,y_2)=(16,24)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values, we get $m=\frac{24 - 12}{16 - 4}=\frac{12}{12}=1$.

Step3: Use the point - slope form to find the equation of the line

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(4,12)$ and $m = 1$, we have $y-12=1\times(x - 4)$. Simplifying gives $y=x + 8$.

Step4: Predict the value for $x = 8$

Substitute $x = 8$ into the equation $y=x + 8$. So $y=8 + 8=16$.

Answer:

(a) $y=x + 8$ (b) $16.00$