Question

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

Answer 1

See a solution process below:

Explanation:

First, solve for two points which solve the equation and plot these points:

First Point: For `x = 2`

`(2 * 2) + 3y = -2`

`4 + 3y = -2`

`4 - color(red)(4) + 3y = -2 - color(red)(4)`

`0 + 3y = -6`

`3y = -6`

`(3y)/color(red)(3) = -6/color(red)(3)`

`y = -2` or `(2, -2)`

Second Point: For `y = 0`

`2x + (3 * 0) = -2`

`2x + 0 = -2`

`2x = -2`

`(2x)/color(red)(2) = -2/color(red)(2)`

`x = -1` or `(-1, 0)`

We can next plot the two points on the coordinate plane:

graph{((x-2)^2+(y+2)^2-0.04)((x+1)^2+y^2-0.04)=0 [-10, 10, -5, 5]}

Now, we can draw a straight line through the two points to graph the line:

graph{((x-2)^2+(y+2)^2-0.04)((x+1)^2+y^2-0.04)(2x + 3y + 2)=0 [-10, 10, -5, 5]}