y>-4x+10 sketch graph of linear inequality

Question

sketch graph of linear inequality

Answer 1

Given linear inequlity y > -4x+10

y = -4x+10

Now it is in  slope intercept form y = mx+b.

Now sketch the line y = -4x+10

The graph boundary line of y = 4x+10 is shaded dashed line with red colour.

Observe the graph shaded with aqua colour is indicating y > -4x+10.

Comments

To determine which side (left side or right side) to be shaded, use a test point to the left or right side of the line y = -4x + 10.

A simple choice is (0, 0).

Substitute the value of (x, y) = (0, 0) in the original inequality.

0 > -4(0) + 10

0 > 0 + 10

0 > 10 (False)

So shade the other region which doesnot contain the point (0,0).

That is the reason why it is shaded right side part in the graph.