Question

Space provided.

1. Find the equation of the line that is modeled by the values in the table shown below.

Part I: Determine the slope of the line. Show the work you did to find the slope. (6 points)

Answer 1

1) The slope of the line is
`m=(5)/(2)` or
`m=2.5`

2) The equation of the line is
`y=2.5x-4`

Explanation:

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

take any two points from the values in the table

(2,1) and (4,6)

substitute the values in the formula

`m=(6-1)/(4-2)`

`m=(5)/(2)`

`m=2.5`

step 2

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

we have

`m=2.5`

`point\ (2,1)`

substitute

`y-1=2.5(x-2)`

Convert to slope intercept form

isolate the variable y

`y-1=2.5x-5`

`y=2.5x-5+1`

`y=2.5x-4`