Question

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.)
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 =
(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

Explanation:

Step1: Assume the line of best - fit equation

The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We can use two points on the line of best - fit (estimated from the scatter - plot) to find $m$ and $b$. Let's assume two points $(x_1,y_1)$ and $(x_2,y_2)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Estimate points from the scatter - plot

Suppose we estimate two points on the line of best - fit as $(5,20)$ and $(20,10)$. Then $m=\frac{10 - 20}{20 - 5}=\frac{- 10}{15}\approx - 0.67$.
To find $b$, we substitute one of the points, say $(5,20)$, into $y=-0.67x + b$. So $20=-0.67\times5 + b$, which gives $b=20 + 0.67\times5=20 + 3.35 = 23.35$. The equation of the line of best - fit is $y=-0.67x + 23.35$.

Step3: Make a prediction

We are asked to predict $y$ when $x = 12$. Substitute $x = 12$ into the equation $y=-0.67\times12+23.35$.
$y=-8.04 + 23.35=15.31$.

Answer:

(a) $y=-0.67x + 23.35$
(b) $15.31$