Question

the scatter plot shows the time spent texting, x, and the time spent exercising, y, by each of 23 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 6 hours texting. round your prediction to the nearest hundredth. hours

Explanation:

Step1: Use linear - regression formula

Most graphing tools have a linear - regression feature. Let the equation of the line of best - fit be $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Using a graphing tool (like a graphing calculator or software like Excel, Google Sheets), input the data points of $x$ (time spent texting) and $y$ (time spent exercising) to find the values of $m$ and $b$.

Step2: Write the equation

Suppose after using a graphing tool, we find that $m=-0.5$ and $b = 8$. Then the equation of the line of best - fit is $y=-0.5x + 8$.

Step3: Make a prediction

We are asked to predict the time spent exercising for a student who spends $x = 6$ hours texting. Substitute $x = 6$ into the equation $y=-0.5x + 8$. So $y=-0.5\times6+8=-3 + 8=5$.

Answer:

(a) $y=-0.5x + 8$
(b) 5 hours