Algebra Examples

$y \geq 2 x^{2} - 4$ $y < - 0.5 x - 1$ $y < 3 x + 2$

Step 1

Graph $y \geq 2 x^{2} - 4$ .

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Step 1.1

The equation is not linear, so a constant slope does not exist.

Not Linear

Step 1.2

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $2 x^{2} - 4$ .

$y \geq 2 x^{2} - 4$

Step 2

Graph $y < - 0.5 x - 1$ .

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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 $y = m x + b$ .

$m = - 0.5$

$b = - 1$

Step 2.1.3

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

Slope: $- 0.5$

y-intercept: $(0, - 1)$

Slope: $- 0.5$

y-intercept: $(0, - 1)$

Step 2.2

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- 0.5 x - 1$ .

$y < - 0.5 x - 1$

Step 3

Graph $y < 3 x + 2$ .

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Step 3.1

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

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Step 3.1.1

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 3.1.2

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

$m = 3$

$b = 2$

Step 3.1.3

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

Slope: $3$

y-intercept: $(0, 2)$

Slope: $3$

y-intercept: $(0, 2)$

Step 3.2

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $3 x + 2$ .

$y < 3 x + 2$

Step 4

Plot each graph on the same coordinate system.

$y \geq 2 x^{2} - 4$

$y < - 0.5 x - 1$

$y < 3 x + 2$

Step 5