Algebra Examples

$x + y > 0$ $x + y + 5 < 0$

Step 1

Graph $x + y > 0$ .

Tap for more steps...

Step 1.1

Subtract $x$ from both sides of the inequality.

$y > - x$

Step 1.2

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

Tap for more steps...

Step 1.2.1

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

$y = m x + b$

Step 1.2.2

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

$m = - 1$

$b = 0$

Step 1.2.3

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

Slope: $- 1$

y-intercept: $(0, 0)$

Slope: $- 1$

y-intercept: $(0, 0)$

Step 1.3

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

$y > - x$

Step 2

Graph $x + y + 5 < 0$ .

Tap for more steps...

Step 2.1

Move all terms not containing $y$ to the right side of the inequality.

Tap for more steps...

Step 2.1.1

Subtract $x$ from both sides of the inequality.

$y + 5 < - x$

Step 2.1.2

Subtract $5$ from both sides of the inequality.

$y < - x - 5$

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

$y = m x + b$

Step 2.2.2

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

$m = - 1$

$b = - 5$

Step 2.2.3

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

Slope: $- 1$

y-intercept: $(0, - 5)$

Slope: $- 1$

y-intercept: $(0, - 5)$

Step 2.3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- x - 5$ .

$y < - x - 5$

Step 3

Plot each graph on the same coordinate system.

$x + y > 0$

$x + y + 5 < 0$

Step 4