Question

Complete the point-slope equation of the line through (0, -1) and (1, 2)

Answer 1

`y+1=3x`

OR

`y-2=3(x-1)`

Explanation:

Hi there!

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

1) Determine the slope (m)

`m=\displaystyle (y_2-y_1)/(x_2-x_1)` where two points that fall on the line are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the points (0,-1) and (1,2):

`m=\displaystyle (2-(-1))/(1-0)\\\\m=\displaystyle (2+1)/(1)\\\\m=3`

Therefore, the slope of the line is 3. Plug this into
`y-y_1=m(x-x_1)`:

`y-y_1=3(x-x_1)`

2) Plug a point into the equation

`y-y_1=3(x-x_1)`

Because we're given two points, there are two ways we can write the equation:

`y-y_1=3(x-x_1)y-(-1)=3(x-0)\\y+1=3x`

OR

`y-y_1=3(x-x_1)\\y-2=3(x-1)`

I hope this helps!