Question

The scatter plot shows the time spent texting,x , and the time spent exercising,y , by each of 23 students last week.

(a) Write an approximate equation of the line of best fit for the data. It doesn't have to be the exact line of best fit.

(b) Using your equation from part (a), predict the time spent exercising for a student who spends hours texting.

Note that you can use the graphing tools to help you approximate the line. also points are 9,1 and 10,1

Answer 1

The lines of best fit show the relationship between the hours spent on texting and exercising.

• The equation of the line of best fit is $\mathbf{y = -0.73x + 8.65 }$
• The time spent exercising for a student who spends 6 hours texting is 4.27 hours

(a) The equation of line of best fit

From the graph (see attachment), we have the following points:

$\mathbf{(x,y) = (5,5),\ (2,7.2)}$

The slope of the line is:

$\mathbf{m = \frac{y_2 - y_1}{x_2 - x_1}}$

So, we have:

$\mathbf{m = \frac{7.2-5}{2-5}}$

$\mathbf{m = \frac{2.2}{-3}}$

$\mathbf{m = -0.73}$

The equation is then calculated as:

$\mathbf{y = m(x - x_1) + y_1}$

This gives:

$\mathbf{y = -0.73(x - 5) + 5}$

$\mathbf{y = -0.73x + 3.65 + 5}$

$\mathbf{y = -0.73x + 8.65 }$

Hence, the equation of the line of best fit is $\mathbf{y = -0.73x + 8.65 }$

(b) The time spent exercising for a student who spends 6 hours texting

This means that x = 6.

So, we have:

$\mathbf{y = -0.73 \times 6 + 8.65 }$

$\mathbf{y = -4.38 + 8.65 }$

$\mathbf{y = 4.27 }$

Hence, the time spent exercising for a student who spends 6 hours texting is 4.27 hours

Read more about lines of best fit at:

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