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

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

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

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

The equation of trend line is

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 .

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b