Algebra Examples

$2 x + y \geq 2$ $2 x + y < 4$

Step 1

Graph $2 x + y \geq 2$ .

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Step 1.1

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

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Step 1.1.1

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

$y \geq 2 - 2 x$

Step 1.1.2

Rearrange terms.

$y \geq - 2 x + 2$

Step 1.2

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

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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 $y = m x + b$ .

$m = - 2$

$b = 2$

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: $(0, 2)$

Slope: $- 2$

y-intercept: $(0, 2)$

Step 1.3

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 2

Graph $2 x + y < 4$ .

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Step 2.1

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

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Step 2.1.1

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

$y < 4 - 2 x$

Step 2.1.2

Rearrange terms.

$y < - 2 x + 4$

Step 2.2

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

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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 $y = m x + b$ .

$m = - 2$

$b = 4$

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: $(0, 4)$

Slope: $- 2$

y-intercept: $(0, 4)$

Step 2.3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- 2 x + 4$ .

$y < - 2 x + 4$

Step 3

Plot each graph on the same coordinate system.

$2 x + y \geq 2$

$2 x + y < 4$

Step 4