# How do you graph the inequality 4x-2y<-3?

Jul 1, 2018

See below

#### Explanation:

$4 x - 2 y < - 3$

Subtract $4 x$ to both sides

$- 2 y < - 4 x - 3$

Divide through by $- 2$ and change the direction of the inequality.

$y > 2 x + \frac{3}{2}$

Now consider the limiting case where: $y = 2 x + \frac{3}{2}$

This is the straight line with slope $2$ and $y -$intercept of $+ \frac{3}{2}$

Then the graphic representation of the inequality is the area of all points where $y$ is greater than but not equal to values on this line. Shown as the shaded area below.

graph{4x-2y<-3 [-12.66, 12.65, -6.33, 6.33]}