Question

How to find the slope and y-intercept for `y-2x<6`?

Answer 1

`y<2x+6`

The slope is `2` and the y-intercept is `6`.

Explanation:

`y-2x<6`

Solve for `y` to get the inequality into slope-intercept form:

`y=mx+b`,

where:

`m` is the slope, and `b` is the y-intercept.

Solve for `y`.

`y-2x<6`

Add `2x` to both sides.

`y<2x+6`

The slope is `2` and the y-intercept is `6`.

Answer 2

`y`-intercept: `(0, 6)`
Slope: `m=2`
The solution for `y` is given by the graph below.

Explanation:

The easiest way to evaluate this inequality is to pretend (for a moment) that we are actually dealing with the equation,

`y-2x = 6`

The `y` intercept of an equation occurs when `x=0`.

`y-2x = 6`

`y-2(0) = 6`

`y = 6`

So the `y`-intercept is the point `(0, 6)`. The `x`-intercept occurs when `y=0`.

`y - 2x = 6`

`0 - 2x = 6`

`-2x = 6`

`x = -3`

So the `x`-intercept is the point `(-3, 0)`. Draw a dashed line through these points to account for the inequality symbol.

The slope is the rise over the run.

`m="rise"/"run"=6/3=2`

Desmos.com and MS Paint

The final step is to determine where to shade by choosing an easy point, like `(0, 0)`. If plugging in this point makes the original inequality a true statement, then shade that entire side of the line.

`y-2x<6`

`0-2(0)<6`

`0 < 6` is true.

So shade the side with the point `(0, 0)`

Desmos.com and MS Paint