Algebra Examples

$\frac{x}{2} + \frac{y}{3} > 1$

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

Subtract $\frac{x}{2}$ from both sides of the inequality.

$\frac{y}{3} > 1 - \frac{x}{2}$

Step 1.1.2

Multiply both sides by $3$ .

$\frac{y}{3} \cdot 3 > (1 - \frac{x}{2}) \cdot 3$

Step 1.1.3

Simplify.

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Step 1.1.3.1

Simplify the left side.

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Step 1.1.3.1.1

Cancel the common factor of $3$ .

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Step 1.1.3.1.1.1

Cancel the common factor.

$\frac{y}{3} \cdot 3 > (1 - \frac{x}{2}) \cdot 3$

Step 1.1.3.1.1.2

Rewrite the expression.

$y > (1 - \frac{x}{2}) \cdot 3$

Step 1.1.3.2

Simplify the right side.

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Step 1.1.3.2.1

Simplify $(1 - \frac{x}{2}) \cdot 3$ .

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Step 1.1.3.2.1.1

Apply the distributive property.

$y > 1 \cdot 3 - \frac{x}{2} \cdot 3$

Step 1.1.3.2.1.2

Multiply $3$ by $1$ .

$y > 3 - \frac{x}{2} \cdot 3$

Step 1.1.3.2.1.3

Multiply $- \frac{x}{2} \cdot 3$ .

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Step 1.1.3.2.1.3.1

Multiply $3$ by $- 1$ .

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

Step 1.1.3.2.1.3.2

Combine $- 3$ and $\frac{x}{2}$ .

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

Step 1.1.3.2.1.4

Move the negative in front of the fraction.

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

Step 1.1.3.2.1.5

Reorder $3$ and $- \frac{3 x}{2}$ .

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

Step 1.2

Reorder terms.

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

Step 1.3

Remove parentheses.

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

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 $y = m x + b$ .

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

$b = 3$

Step 2.2

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

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

y-intercept: $(0, 3)$

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

y-intercept: $(0, 3)$

Step 3

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

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

Step 4