Algebra Examples

$2 x + y \leq 5$ $y + 2 \geq - 2 x$

Step 1

Graph $2 x + y \leq 5$ .

Tap for more steps...

Step 1.1

Write in $y = m x + b$ form.

Tap for more steps...

Step 1.1.1

Subtract $2 x$ from both sides of the inequality.

$y \leq 5 - 2 x$

Step 1.1.2

Rearrange terms.

$y \leq - 2 x + 5$

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 $y = m x + b$ .

$m = - 2$

$b = 5$

Step 1.2.3

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

Slope: $- 2$

y-intercept: $(0, 5)$

Slope: $- 2$

y-intercept: $(0, 5)$

Step 1.3

Graph a solid line, then shade the area below the boundary line since $y$ is less than $- 2 x + 5$ .

$y \leq - 2 x + 5$

Step 2

Graph $y + 2 \geq - 2 x$ .

Tap for more steps...

Step 2.1

Subtract $2$ from both sides of the inequality.

$y \geq - 2 x - 2$

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 $y = m x + b$ .

$m = - 2$

$b = - 2$

Step 2.2.3

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

Slope: $- 2$

y-intercept: $(0, - 2)$

Slope: $- 2$

y-intercept: $(0, - 2)$

Step 2.3

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

$y \geq - 2 x - 2$

Step 3

Plot each graph on the same coordinate system.

$2 x + y \leq 5$

$y + 2 \geq - 2 x$

Step 4