How do you graph the following equation and identify y-intercept `2y+3x= -2`?

1) Put the equation into Slope-Intercept form (`y=mx+b`).

`2y+3x=-2`
`2y+cancel(3x color(red)(-3x))=-2-color(red)(3x)`
`2y=-2-3x`
`color(blue)(-1)*(2y=-2-3x)`

• Note: I multiplied the equation by `color(blue)(-1` to show how you make this equation would resemble the formula. You don't have to do this step for this particular equation though because the answers are negative anyway.

`-2y=2+3x`

• Note: Because of the Commutative Property of Addition you can rearrange the equation to look like the formula

`-2y=3x+2`
`(-2y=3x+2)/-2`
`y=-3/2x+color(green)[(-2/2)`

Now that the equation is in Slope Intercept form (`y=mx+b`) you know the slope (`m`) and the y-intercept (`b`).

2) Find the x-intercept

To find the x-intercept you need to set `y` equal to `0`

• Note: I'm going to use the original equation because it is faster but you could use the new equation too.

`2color(orange)y+3x=-2`
`2color(orange)[(0)]+3x=-2`
`3x=-2`
`(3x=-2)/3`
`x=-2/3`

Now, that you know the following:

• The slope is `-3/2`, this means the graph will be going down or decreasing
• The y-intercept is `-1`, this means the graph crosses the y-axis at the point `(0,-1)`
• The x-intercept is `-2/3`, this means the graph crosses the x-axis at the point `(-2/3, 0)`

You can either:

Plot the coordinates of the x and y-intercepts and use the slope to create a line

OR

Use the Slope Intercept form equation to create points ranging between the two intercepts and then connect the dots