Question

How do you graph the inequality `y< -2/5x+1`?

Answer 1

The slope is `-2/5`.
The y-intercept is `1`. The point is `(0,1)`.
The x-intercept is `2/5`. The point is `(2/5,0)`.

Explanation:

`y<-2/5x+1` is in the slope-intercept form of a linear equation, `y=mx+b`, where `m` is the slope and `b` is the y-intercept. The y-intercept is the value of `y` when `x` is `0`.

Find the `x` and `y` intercepts.

The y-intercept is `+1`.

The point for the y-intercept is `(0,1)`.

Find the `x` intercept by substituting `0` for `y` and solving for `x`.

`0=-2/5x+1`

Subtract `1` from both sides.

`-1=-2/5x`

Multiply both sides by `5`

`5xx-1=-2x`

`-5=-2x`

Divide both sides by `-2`.

`(-5)/(-2)=x`

`5/2=x`

Switch sides.

`x=5/2`

The x-intercept is `5/2`.

The point for the x-intercept is `(5/2,0)`.

Plot the two points on a graph. Draw a straight dashed line through the points to indicate that the line is not part of the inequality. Then shade the area below the line.

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