Pre-Algebra Examples

$3 y > 2 x + 9$

Step 1

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

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Step 1.1

Divide each term in $3 y > 2 x + 9$ by $3$ and simplify.

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Step 1.1.1

Divide each term in $3 y > 2 x + 9$ by $3$ .

$\frac{3 y}{3} > \frac{2 x}{3} + \frac{9}{3}$

Step 1.1.2

Simplify the left side.

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Step 1.1.2.1

Cancel the common factor of $3$ .

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Step 1.1.2.1.1

Cancel the common factor.

$\frac{3 y}{3} > \frac{2 x}{3} + \frac{9}{3}$

Step 1.1.2.1.2

Divide $y$ by $1$ .

$y > \frac{2 x}{3} + \frac{9}{3}$

Step 1.1.3

Simplify the right side.

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Step 1.1.3.1

Divide $9$ by $3$ .

$y > \frac{2 x}{3} + 3$

Step 1.2

Reorder terms.

$y > \frac{2}{3} x + 3$

Step 2

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

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Step 2.1

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

$m = \frac{2}{3}$

$b = 3$

Step 2.2

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

Slope: $\frac{2}{3}$

y-intercept: $(0, 3)$

Slope: $\frac{2}{3}$

y-intercept: $(0, 3)$

Step 3

Graph a dashed line, then shade the area above the boundary line since $y$ is greater than $\frac{2}{3} x + 3$ .

$y > \frac{2}{3} x + 3$

Step 4