Question

How do you graph `-3x-2y=-2`?

Answer 1

Convert the given equation to slope intercept form, `y=mx+b.` Determine points on the line. Plot the points and draw a straight line through them.

Explanation:

Graph:

`-3x-2y=-2`

Solve for `y` to get the equation into slope intercept form: `y=mx+b`, where `m` is the slope and `b` is the y-intercept (the value of `y` when `x=0`).

Add `3x` to both sides of the equation.

`color(red)cancel(color(black)(3x))-color(red)cancel(color(black)(3x))-2y=3x-2`

Simplify.

`-2y=3x-2`

Divide both sides by `-2`.

`(color(red)cancel(color(black)(-2^1y)))/(color(red)cancel(color(black)(-2^1)))=(3x)/(-2)+(color(red)cancel(color(black)(-2^1))/color(red)cancel(color(black)(-2^1)))`

A negative number divided by another negative number gives a positive result.

`y=-3/2x+1`

Now you can determine several points on the line by choosing values for `x` and solving for `y`.

Points

`x=-2,` `y=4`

`x=0,` `y=1`

`x=2,` `y=2`

Plot the points and draw a straight line through them.

graph{-3x-2y=-2 [-10, 10, -5, 5]}