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

1 Answer
Aug 15, 2015

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]}