Question

Use the point-slope formula to write an equation of the line that passes through (-5,3) and

(4,6). Write the answer in slope-intercept form (if possible).

Answer 1

The equation in point slope form is
`y-6=(1)/(3)(x-4)`

The equation in slope intercept form is
`y=(1)/(3)x-(14)/(3)`

Explanation:

step 1

Find the slope m

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

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

we have

`(-5,3),(4,6)`

Substitute the values

`m=(6-3)/(4+5)`

`m=(3)/(9)`

simplify

`m=(1)/(3)`

step 2

Find the equation of the line in point slope form

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

we have

`m=(1)/(3)`

`(4,6)`

substitute

`y-6=(1)/(3)(x-4)` ---> equation in point slope form

step 3

Find the equation of the line in slope intercept form

`y=mx+b`

`y-6=(1)/(3)(x-4)` ----> convert to slope intercept form

`y-6=(1)/(3)x-(4)/(3)`

`y=(1)/(3)x-(4)/(3)+6`

`y=(1)/(3)x-(14)/(3)`