Inequalities and graphs example 2

Graph the following inequality:

$4y-x<=4$

Add $x$ to both sides to get $y$ on its own.

$4y-x<=4$

$4y-x+x<=4+x$

$4y<=4+x$

Divide both sides by 4 to get $y$ on its own.

$(4y)/4<=4/4+x/4$

$y<=1+x/4$

$y<=x/4+1$

First, let's calculate some points on the graph.

Now draw a graph and mark on the above points. Don’t forget to use a SOLID line.

Draw a solid line on the graph

Now pick a point not on the line.

Choose a point not on the line

Choose $x=0$ and $y=0$

$y<=x/4+1$

$0<=0/4+1$

$0<=1$

This read 0 is less than or equal to 1. This is obviously correct.

This DOES satisfy the inequality.

SHADE IT.

If the inequality is satisfied shade in that side