How do I graph this inequality #3x+2y5#?

Question

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

Genesis Allen · Accepted Answer

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]}

Avery Alexander · Answer

undefined To graph the inequality 3x + 2y > 5, follow these steps:

1. Rewrite the inequality in slope-intercept form: y > -(3/2)x + (5/2).
2. Graph the boundary line y = -(3/2)x + (5/2) as a dashed line.
3. Choose a test point not on the boundary line. For example, (0,0) is a common choice.
4. Substitute the coordinates of the test point into the original inequality. If the inequality is true, shade the region containing the test point. If false, shade the opposite region.
5. Draw arrows to indicate which side of the boundary line is shaded.

This will give you the graph of the inequality 3x + 2y > 5.

How do I graph this inequality #3x+2y&gt;5#?

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