Algebra Examples

$y \geq 0$ $y < x$ $x + y < 6$

Step 1

Graph $y \geq 0$ .

$y \geq 0$

Step 2

Graph $y < x$ .

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Step 2.1

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

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Step 2.1.1

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 2.1.2

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

$m = 1$

$b = 0$

Step 2.1.3

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 2.2

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

$y < x$

Step 3

Graph $x + y < 6$ .

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Step 3.1

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

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Step 3.1.1

Subtract $x$ from both sides of the inequality.

$y < 6 - x$

Step 3.1.2

Rearrange terms.

$y < - x + 6$

Step 3.2

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

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Step 3.2.1

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 3.2.2

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

$m = - 1$

$b = 6$

Step 3.2.3

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

Slope: $- 1$

y-intercept: $(0, 6)$

Slope: $- 1$

y-intercept: $(0, 6)$

Step 3.3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- x + 6$ .

$y < - x + 6$

Step 4

Plot each graph on the same coordinate system.

$y \geq 0$

$y < x$

$x + y < 6$

Step 5