How do you graph the inequality y+4x>=3?

Sep 4, 2017

See a solution process below:

Explanation:

First, solve for two points as an equation instead of an inequality to find the boundary line for the inequality.

For: $x = 0$

$y + \left(4 \cdot 0\right) = 3$

$y + 0 = 3$

$y = 3$

$y = 3$ or $\left(0 , 3\right)$

For: $x = 2$

$y + \left(4 \cdot 2\right) = 3$

$y + 8 = 3$

$y + 8 - \textcolor{red}{8} = 3 - \textcolor{red}{8}$

$y + 0 = - 5$

$y = - 5$ or $\left(2 , - 5\right)$

We can now graph the two points on the coordinate plane and draw a line through the points to mark the boundary of the inequality.

The boundary line will be solid because the inequality operator contains a "or equal to" clause.

graph{(x^2+(y-3)^2-0.05)((x-2)^2+(y+5)^2-0.05)(4x+y-3)=0 [-15, 15, -7.5, 7.5]}

Now, we can shade the right side of the line.

graph{(4x+y-3)>=0 [-15, 15, -7.5, 7.510]}