Algebra Examples

$y < 3 x + 8$ $y \geq 4 x$

Step 1

Graph $y < 3 x + 8$ .

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Step 1.1

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

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Step 1.1.1

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 1.1.2

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

$m = 3$

$b = 8$

Step 1.1.3

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

Slope: $3$

y-intercept: $(0, 8)$

Slope: $3$

y-intercept: $(0, 8)$

Step 1.2

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $3 x + 8$ .

$y < 3 x + 8$

Step 2

Graph $y \geq 4 x$ .

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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 $y = m x + b$ .

$m = 4$

$b = 0$

Step 2.1.3

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

Slope: $4$

y-intercept: $(0, 0)$

Slope: $4$

y-intercept: $(0, 0)$

Step 2.2

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $4 x$ .

$y \geq 4 x$

Step 3

Plot each graph on the same coordinate system.

$y < 3 x + 8$

$y \geq 4 x$

Step 4