Question

How do you graph -2x + 3y = 12 on a coordinate graph?

Answer 1

Convert the equation to slope-intercept form. Use the equation to find two points. Plot the points and draw a straight line through the points.

Explanation:

`-2x+3y=12` follows the standard form for a linear equation, `Ax+By=C`.

In order to graph this equation, you need to convert it to the slope-intercept form, and solve fore `y`. The slope-intercept form for a linear equation is `y=mx+b`, where `m` is the slope, and `b` is the slope-intercept.

Convert the Standard Equation to Slope-intercept Form

`-2x+3y=12`

Add `2x` to both sides of the equation.

`3y=2x+12`

Divide both sides by `3`.

`y=2/3x+12/3` =

`y=2/3x+4`

Now use the equation to find two points on the line. Plot them, then draw a straight line through the points.

Point A: `(0,4)`

If `x=0, y=4`

`y=2/3x+4` =

Substitute `0` for `x`.

`y=2/3(0)+4` =

`y=0+4=4` =

`y=4`

Point B: `(-6,0)`

If `y=0, y=-6`

`y=2/3x+4`

Substitute `0` for `y`.

`0=2/3x+4`

Subtract `4` from both sides.

`-4=2/3x`

Divide both sides by `2/3`.

`-4/1-:2/3=x` =

`-4/1xx3/2=x` =

`-12/2=x` =

`-6=x`

graph{y=2/3x+4 [-10, 10, -5, 5]}