Algebra Examples

y \geq 2 x^{2} - 4

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

y < - 0.5 x - 1

$y < - 0.5 x - 1$

y < 3 x + 2

$y < 3 x + 2$

Step 1

Graph

y \geq 2 x^{2} - 4

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

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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

$y$ is greater than

2 x^{2} - 4

$2 x^{2} - 4$ .

y \geq 2 x^{2} - 4

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

y \geq 2 x^{2} - 4

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

Step 2

Graph

y < - 0.5 x - 1

$y < - 0.5 x - 1$ .

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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

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 2.1.2

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = - 0.5

$m = - 0.5$

b = - 1

$b = - 1$

Step 2.1.3

The slope of the line is the value of

m

$m$ , and the y-intercept is the value of

b

$b$ .

Slope:

- 0.5

$- 0.5$

y-intercept:

(0, - 1)

$(0, - 1)$

Slope:

- 0.5

$- 0.5$

y-intercept:

(0, - 1)

$(0, - 1)$

Step 2.2

Graph a dashed line, then shade the area below the boundary line since

y

$y$ is less than

- 0.5 x - 1

$- 0.5 x - 1$ .

y < - 0.5 x - 1

$y < - 0.5 x - 1$

y < - 0.5 x - 1

$y < - 0.5 x - 1$

Step 3

Graph

y < 3 x + 2

$y < 3 x + 2$ .

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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

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 3.1.2

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = 3

$m = 3$

b = 2

$b = 2$

Step 3.1.3

The slope of the line is the value of

m

$m$ , and the y-intercept is the value of

b

$b$ .

Slope:

3

$3$

y-intercept:

(0, 2)

$(0, 2)$

Slope:

3

$3$

y-intercept:

(0, 2)

$(0, 2)$

Step 3.2

Graph a dashed line, then shade the area below the boundary line since

y

$y$ is less than

3 x + 2

$3 x + 2$ .

y < 3 x + 2

$y < 3 x + 2$

y < 3 x + 2

$y < 3 x + 2$

Step 4

Plot each graph on the same coordinate system.

y \geq 2 x^{2} - 4

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

y < - 0.5 x - 1

$y < - 0.5 x - 1$

y < 3 x + 2

$y < 3 x + 2$

Step 5