How do you graph the inequality #2x-3y<=1# on the coordinate plane?

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Answer 1 · 2017-04-26T09:31:11

Draw the line and decide which side to shade for the required region.

Treat the inequality as a straight line graph first .
Then shade the correct side of the line to indicate the solutions which are less than #1#

You can use any method to draw the straight line - plot points or use the intercept/gradient method.

I will use the method of the #x and y# intercepts.

To find the #x#-intercept, make #y=0#

#2x-3y =1" "rarr 0 -3y = 1#

#color(blue)(y = -1/3)#

To find the #y#-intercept, make #x=0#

#2x-3y =1" "rarr 2x -0 = 1#

#color(blue)(x = 1/2)#

Now that you have both intercepts you can plot them and draw a solid line through them. This is the line #2x-3y =1#

You could also write the equation as : #y = 2/3x-1/3#

To decide which side of the line to shade, choose a test point.

#(0,0)# is a good one.

#2x-3y <=1" "rarr" " 0-0 <=1" "rarr" " 0 <=1# is true.

#:. (0,0)# is in the required region and the area ABOVE the line must be shaded. graph{2x-3y<=1 [-10, 10, -5, 5]}