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

Nov 2, 2015

The slope is $- \frac{2}{5}$.
The y-intercept is $1$. The point is $\left(0 , 1\right)$.
The x-intercept is $\frac{2}{5}$. The point is $\left(\frac{2}{5} , 0\right)$.

#### Explanation:

$y < - \frac{2}{5} x + 1$ is in the slope-intercept form of a linear equation, $y = m x + b$, 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 $\left(0 , 1\right)$.

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

$0 = - \frac{2}{5} x + 1$

Subtract $1$ from both sides.

$- 1 = - \frac{2}{5} x$

Multiply both sides by $5$

$5 \times - 1 = - 2 x$

$- 5 = - 2 x$

Divide both sides by $- 2$.

$\frac{- 5}{- 2} = x$

$\frac{5}{2} = x$

Switch sides.

$x = \frac{5}{2}$

The x-intercept is $\frac{5}{2}$.

The point for the x-intercept is $\left(\frac{5}{2} , 0\right)$.

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]}