How do I graph this inequality #3x+2y>5#?

1 Answer
Stefan V.
Apr 16, 2015

Start by isolating #y# on the left side of the inequality

#3x + 2y > 5#

#2y > -2x + 5 |:2#

#y > -3/2x + 5/2#

Now calculate the x and y-intercepts by making #y=0# (for the x-intercept), and then #x=0# (for the y-intercept).

These two points will allow you to draw the line

#y = -3/2x + 5/2#

So,

#x = 0 => y = +5/2#

#y = 0 => 0 = -3/2x + 5 => x = 5/3#

Here's how that line would look

graph{-3/2x + 5/2 [-10, 10, -5, 5]}

However, since your inequality requires that #y# be greater than#-3/2x + 5/2#, the solution region you're interested in must be above the line and not include the line.

You'll end up with a graph in which you have a dashed line and the shaded region above that line.

graph{y > -3/2x + 5/2 [-10, 10, -5, 5]}

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