Algebra Examples

$y + x < 3$ $y - x \geq 1$

Step 1

Graph $y + x < 3$ .

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Step 1.1

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

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Step 1.1.1

Subtract $x$ from both sides of the inequality.

$y < 3 - x$

Step 1.1.2

Rearrange terms.

$y < - x + 3$

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 $y = m x + b$ .

$m = - 1$

$b = 3$

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: $(0, 3)$

Slope: $- 1$

y-intercept: $(0, 3)$

Step 1.3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- x + 3$ .

$y < - x + 3$

Step 2

Graph $y - x \geq 1$ .

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Step 2.1

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

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Step 2.1.1

Add $x$ to both sides of the inequality.

$y \geq 1 + x$

Step 2.1.2

Rearrange terms.

$y \geq x + 1$

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 $y = m x + b$ .

$m = 1$

$b = 1$

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: $(0, 1)$

Slope: $1$

y-intercept: $(0, 1)$

Step 2.3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $x + 1$ .

$y \geq x + 1$

Step 3

Plot each graph on the same coordinate system.

$y + x < 3$

$y - x \geq 1$

Step 4