Question

How do you graph the inequality `y< 2x - 1`?

Answer 1

Refer to the explanation.

Explanation:

Graph:

`y<2x-1`

Find the x- and y-intercepts.

X-intercept: value of `x` when `y=0`

Substitute an equal sign for the less than symbol.

`y=2x-1`

Substitute `0` for `y`.

`0=2x-1`

Add `1` to both sides.

`1=2x`

Divide both sides by `2`.

`1/2=x`

The x-intercept is `(1/2,0)`.

Y-intercept: value of `y` when `x=0`

Substitute `0` for `x`.

`y=2(0)-1`

`y=-1`

The y-intercept is `(0,-1)`

Plot the points. Draw a dashed line through the points. This indicates that the line is not a part of the inequality. Since `y<2x-1`, shade in the area below the line.

graph{y<2x-1 [-10, 10, -5, 5]}