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

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Answer 1 · 2018-01-20T22:12:53

See a solution process below:

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]}