the scatter plot shows the time spent texting, x, and the time spent exercising, y, by each of 25 students…

the scatter plot shows the time spent texting, x, and the time spent exercising, y, by each of 25 students last week. 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 time spent exercising for a student who spends 4 hours texting. round your prediction to the nearest hundredth. hours

the scatter plot shows the time spent texting, x, and the time spent exercising, y, by each of 25 students last week. 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 time spent exercising for a student who spends 4 hours texting. round your prediction to the nearest hundredth. hours

Answer

Explanation:

Step1: Select two points on the line

Let's assume two points on the approximated line of best - fit: $(x_1,y_1)=(2,7)$ and $(x_2,y_2)=(6,3)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{3 - 7}{6 - 2}=\frac{-4}{4}=-1$.

Step3: Find the y - intercept $b$

Using the point - slope form $y - y_1=m(x - x_1)$ with the point $(2,7)$ and $m=-1$, we have $y-7=-1(x - 2)$. Expanding gives $y-7=-x + 2$, and then $y=-x+9$.

Step4: Predict for $x = 4$

Substitute $x = 4$ into the equation $y=-x + 9$. So, $y=-4 + 9=5$.

Answer:

(a) $y=-x + 9$ (b) $5$