Question

How do you graph the inequality `y>x-3`?

Answer 1

First, you plot the line `y = x-3`. It has a gradient of 1, so for every 1 unit along you go, you go up one unit. It has a y-intercept of -3, so it will touch the y-axis at the point `y=-3`.

When you draw this line, make it dashed, because it is a strict inequality, which is represented by a dashed line
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The region which satisfies the inequality (which you may want to shade) will be the region above the line which you have drawn. It is above the line because the inequality is `>`, so to satisfy it the y-value must be greater than the x-value -3.

You can check you've done it right by picking a point in the shaded region and testing it in the inequality.