Question

What is an equation in point-slope form of the line that passes through (-7.1) and (-3.9)?

Answer 1

`y-1=2(x+7)`

Explanation:

Point-slope form:
`y-y_1=m(x-x_1)` where a given point is
`(x_1,y_1)` and the slope is
`m`

1) Find the slope of the line (m)

Slope =
`(y_2-y_1)/(x_2-x_1)` where the given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the points (-7,1) and (-3,9)

`= (9-1)/(-3-(-7))\\= (8)/(-3+7)\\= (8)/(4)\\= 2`

Therefore, the slope of the line is 2. Plug 2 into the equation as m:

`y-y_1=2(x-x_1)`

2) Plug one of the given points into the equation

We plan either plug in (-7,1) or (-3,9) and it would work either way. Below you can see the equation plugging in the point (-7,1):

`y-1=2(x-(-7))\\y-1=2(x+7)`

I hope this helps!