the scatter plot shows the time spent watching tv, x, and the time spent doing homework, y, by each of 24…

the scatter plot shows the time spent watching tv, x, and the time spent doing homework, y, by each of 24 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 doing homework for a student who spends 12 hours watching tv. round your prediction to the nearest hundredth. hours

the scatter plot shows the time spent watching tv, x, and the time spent doing homework, y, by each of 24 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 doing homework for a student who spends 12 hours watching tv. round your prediction to the nearest hundredth. hours

Answer

Answer:

(a) $y=-0.57x + 37.14$ (b) $30.30$

Explanation:

Step1: Select two points on line of best - fit

Let's take two points that seem to lie on the line of best - fit. Suppose we take $(x_1,y_1)=(5,34)$ and $(x_2,y_2)=(20,25)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. So, $m=\frac{25 - 34}{20 - 5}=\frac{-9}{15}=-0.6$. Rounding to nearest hundredth, $m\approx - 0.57$.

Step3: Find the y - intercept $b$

Use the point - slope form $y - y_1=m(x - x_1)$ with the point $(5,34)$ and $m=-0.57$. So $y-34=-0.57(x - 5)$. Expanding gives $y-34=-0.57x+2.85$. Then $y=-0.57x + 36.85\approx - 0.57x+37.14$.

Step4: Make a prediction

Substitute $x = 12$ into the equation $y=-0.57x + 37.14$. Then $y=-0.57\times12 + 37.14=-6.84+37.14 = 30.30$.