Question

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

Answer 1

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

Explanation:

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]}