Question

How do you graph the equation `y<=2x+3`?

Answer 1

First, find two points which solve the this if it is written as an equation and plot these two points on the grid then draw a line through the two points:

For `x = 0`:

`y = (2 * 0) + 3`

`y = 0 + 3`

`y = 3` or `(0, 3)`

For `x = 2`:

`y = (2 * 2) + 3`

`y = 4 + 3`

`y = 7` or `(2, 7)`

graph{(y - 2x - 3)(x^2 + (y-3)^2 - 0.125)((x - 2)^2 + (y - 7)^2 - 0.125) = 0 [-20, 20, -10, 10]}

Because the inequality is "less than or equal to" we can draw a solid line through the two points. And, also because it is "less than or equal to" we need to shade below the line.

graph{(y - 2x - 3) <= 0 [-20, 20, -10, 10]}