Pre-Algebra Examples

$- 6 x + 3 y \geq - 45$

Step 1

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

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Add $6 x$ to both sides of the inequality.

$3 y \geq - 45 + 6 x$

Step 1.1.2

Divide each term in $3 y \geq - 45 + 6 x$ by $3$ and simplify.

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Step 1.1.2.1

Divide each term in $3 y \geq - 45 + 6 x$ by $3$ .

$\frac{3 y}{3} \geq \frac{- 45}{3} + \frac{6 x}{3}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $3$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{3 y}{3} \geq \frac{- 45}{3} + \frac{6 x}{3}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y \geq \frac{- 45}{3} + \frac{6 x}{3}$

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide $- 45$ by $3$ .

$y \geq - 15 + \frac{6 x}{3}$

Step 1.1.2.3.1.2

Cancel the common factor of $6$ and $3$ .

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Step 1.1.2.3.1.2.1

Factor $3$ out of $6 x$ .

$y \geq - 15 + \frac{3 (2 x)}{3}$

Step 1.1.2.3.1.2.2

Cancel the common factors.

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Step 1.1.2.3.1.2.2.1

Factor $3$ out of $3$ .

$y \geq - 15 + \frac{3 (2 x)}{3 (1)}$

Step 1.1.2.3.1.2.2.2

Cancel the common factor.

$y \geq - 15 + \frac{3 (2 x)}{3 \cdot 1}$

Step 1.1.2.3.1.2.2.3

Rewrite the expression.

$y \geq - 15 + \frac{2 x}{1}$

Step 1.1.2.3.1.2.2.4

Divide $2 x$ by $1$ .

$y \geq - 15 + 2 x$

Step 1.2

Rearrange terms.

$y \geq 2 x - 15$

Step 2

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

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Step 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 2.2

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

$m = 2$

$b = - 15$

Step 2.3

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

Slope: $2$

y-intercept: $(0, - 15)$

Slope: $2$

y-intercept: $(0, - 15)$

Step 3

Graph a solid line, then shade the area above the boundary line since $y$ is greater than $2 x - 15$ .

$y \geq 2 x - 15$

Step 4