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