Graph 2-y<x

$2 - y < x$

Step 1

Solve for $y$ .

Subtract $2$ from both sides of the inequality.

$- y < x - 2$

Divide each term in $- y < x - 2$ by $- 1$ and simplify.

Divide each term in $- y < x - 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- y}{- 1} > \frac{x}{- 1} + \frac{- 2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} > \frac{x}{- 1} + \frac{- 2}{- 1}$

Divide $y$ by $1$ .

$y > \frac{x}{- 1} + \frac{- 2}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$y > - 1 \cdot x + \frac{- 2}{- 1}$

Rewrite $- 1 \cdot x$ as $- x$ .

$y > - x + \frac{- 2}{- 1}$

Divide $- 2$ by $- 1$ .

$y > - x + 2$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - 1$

$b = 2$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- 1$

y-intercept: $(0, 2)$

Slope: $- 1$

y-intercept: $(0, 2)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $- x + 2$ .

$y > - x + 2$

Step 4

Graph 2-y<x

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