Question

How do you write an equation of a line given (-1, 2) and (3, -4)?

Answer 1

`3x+2y+1=0`

Explanation:

Standard form of equation with two points given is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`
`(y-(-4))/(2-(-4))=(x-3)/(-1-3)`

`(y+4)/6=(x-3)/(-4)`
`-4y-16= 6x - 18`

`6x+4y=2`
`3x+2y=1`

Answer 2

`y=-3/2x+1/2`

Explanation:

Okay so there are 3 main forms you can use:
- slope-intercept form [`y=mx+b`]
- standard form [`Ax+By=C`]
- point-slope form [`y_1-y_2=m(x_1-x_2)`]

Since you did not specify which form you wanted it in, I am going to use slope-intercept form because that's the easiest to understand, in my opinion. (:

`y=mx+b`

SLOPE (`m`)
To find `m` (slope), you need to find `(rise)/(run)`, or which is the change in `y` divided by the change in `x`. Use this formula: `(y_1-y_2)/(x_1-x_2)`
`(-1, 2) = (x_1, y_1)`
`(3, -4) = (x_2, y_2)`

It doesn't matter which coordinate pair you choose to be `(x_1, y_1)` or `(x_2, y_2)`. Just stay consistent!

`m = [2-(-4)]/[-1-3] = (2+4)/(-1-3) = 6/-4 = -3/2`
`m`= -3/2#

Y-INTERCEPT (`b`)
Choose one of the coordinates to substitute into `y=mx+b`, which will be substituting for `x` and `y`.
I chose `(-1, 2)`. Substitute `m` for `-3/2`.
`(2)=(-3/2)(-1)+b`
Solve for `b`.
`2=3/2+b`
`b=1/2`

FINAL FORM
Substitute `m` and `b` for their values. This is your answer!
`y=-3/2x+1/2`