Algebra Examples

$2 y < - 12 x + 4$ $y < - 6 x + 4$

Step 1

Graph $2 y < - 12 x + 4$ .

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Step 1.1

Divide each term in $2 y < - 12 x + 4$ by $2$ and simplify.

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Step 1.1.1

Divide each term in $2 y < - 12 x + 4$ by $2$ .

$\frac{2 y}{2} < \frac{- 12 x}{2} + \frac{4}{2}$

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Cancel the common factor of $2$ .

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Step 1.1.2.1.1

Cancel the common factor.

$\frac{2 y}{2} < \frac{- 12 x}{2} + \frac{4}{2}$

Step 1.1.2.1.2

Divide $y$ by $1$ .

$y < \frac{- 12 x}{2} + \frac{4}{2}$

Step 1.1.3

Simplify the right side.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Cancel the common factor of $- 12$ and $2$ .

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Step 1.1.3.1.1.1

Factor $2$ out of $- 12 x$ .

$y < \frac{2 (- 6 x)}{2} + \frac{4}{2}$

Step 1.1.3.1.1.2

Cancel the common factors.

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Step 1.1.3.1.1.2.1

Factor $2$ out of $2$ .

$y < \frac{2 (- 6 x)}{2 (1)} + \frac{4}{2}$

Step 1.1.3.1.1.2.2

Cancel the common factor.

$y < \frac{2 (- 6 x)}{2 \cdot 1} + \frac{4}{2}$

Step 1.1.3.1.1.2.3

Rewrite the expression.

$y < \frac{- 6 x}{1} + \frac{4}{2}$

Step 1.1.3.1.1.2.4

Divide $- 6 x$ by $1$ .

$y < - 6 x + \frac{4}{2}$

Step 1.1.3.1.2

Divide $4$ by $2$ .

$y < - 6 x + 2$

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 $y = m x + b$ .

$m = - 6$

$b = 2$

Step 1.2.3

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

Slope: $- 6$

y-intercept: $(0, 2)$

Slope: $- 6$

y-intercept: $(0, 2)$

Step 1.3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- 6 x + 2$ .

$y < - 6 x + 2$

Step 2

Graph $y < - 6 x + 4$ .

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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 $y = m x + b$ .

$m = - 6$

$b = 4$

Step 2.1.3

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

Slope: $- 6$

y-intercept: $(0, 4)$

Slope: $- 6$

y-intercept: $(0, 4)$

Step 2.2

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $- 6 x + 4$ .

$y < - 6 x + 4$

Step 3

Plot each graph on the same coordinate system.

$2 y < - 12 x + 4$

$y < - 6 x + 4$

Step 4