Write and interpret linear equations

Question

Gus records the mileage on his car so he can determine the average mileage per month. Below are some of his collected data. The table shows TIME (MONTHS) with the numbers 1,2,3,4,5 and 6 listed. And below is MILEAGE (MILES ) with the numbers 11,540 12,482 13,570 14,670 15,682 and 16,757 listed.

1.What is a linear equation that best fits this situation? 2.What is Gus ' mileage after 9 months

Answer 1

Elizabeth

If you have a TI-84 put the numbers into list 1, and the mileages into list 2.

Then stat calc 4 (linear regression).

a = 1051, b = 10438.3 so model is mileage = 1051 x time + 10438.3

r = 0.9998 which tells you that the model predicts very well the mileages (r = 1 for a perfect fit).

You can also plot the data yourself (x = time, y = mileage) and draw a line of best fit by eye and use that.

So after 9 months just put time = 9 into this model.

Mike

Answer 2

x y

time. mileage

1. 11,540

2 12,482

3 13,570

4. 14,670

5 15,682

6 16,757

Consider the time your x and the mileage the y.

First we need to find the slope of the equation.

Recall the equation of a slope is

y₂-y₁

m = ----------

x₂-x₁

Let's use the first two pairs of points.

m = 12482-11540. 942

------------------ =. ----- = 942

2-1. 1

Now use the point-slope form of an equation of a line to find the line

y-y₁=m(x-x₁)

y-11540 = 942(x-1)

distribute

y-11540 = 942x - 942

add the 11540 to both sides

y = 942x + 10598