Question

12. Each day, Yumiko exercises by first doing sit-ups and then running. Make a scatter plot of the total time she exercises as a function of the distance she runs. Draw a trend line.

Distance: 2, 2.5, 3, 3.5, 4
Time: 23, 28, 34, 34, 40

Answer 1

Given:

Distance:   2      2.5    3    3.5    4

Time:        23      28    34   34   40

To find:

The scatter plot of the total time she exercises as a function of the distance she runs.

Solution:

Let y be the total time she exercise if she cover the distance x units..

From the given table, the ordered pairs are (2,23), (2.5,28), (3,34), (3.5,34) and (4,40).

Plot these points on a coordinate plane to get the scatter plot.

Now, the general equation of trend line is

$y=mx+b$

where, a is slope and b is y-intercept.

Using graphing calculator, we get the trend line and value of slope and y-intercept.

$m=8, b=7.8$

The equation of trend line is

$y=8x+7.8$

Therefore, the scatter plot of the total time she exercises as a function of the distance she runs is shown below and the equation of trend line is $y=8x+7.8$.