Algebra Examples

$3 x - 4 y + 5 > 0$

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

Move all terms not containing $y$ to the right side of the inequality.

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Step 1.1.1.1

Subtract $3 x$ from both sides of the inequality.

$- 4 y + 5 > - 3 x$

Step 1.1.1.2

Subtract $5$ from both sides of the inequality.

$- 4 y > - 3 x - 5$

Step 1.1.2

Divide each term in $- 4 y > - 3 x - 5$ by $- 4$ and simplify.

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Step 1.1.2.1

Divide each term in $- 4 y > - 3 x - 5$ by $- 4$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 4 y}{- 4} < \frac{- 3 x}{- 4} + \frac{- 5}{- 4}$

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Cancel the common factor of $- 4$ .

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Step 1.1.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} < \frac{- 3 x}{- 4} + \frac{- 5}{- 4}$

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

$y < \frac{- 3 x}{- 4} + \frac{- 5}{- 4}$

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

Dividing two negative values results in a positive value.

$y < \frac{3 x}{4} + \frac{- 5}{- 4}$

Step 1.1.2.3.1.2

Dividing two negative values results in a positive value.

$y < \frac{3 x}{4} + \frac{5}{4}$

Step 1.2

Reorder terms.

$y < \frac{3}{4} x + \frac{5}{4}$

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 $y = m x + b$ .

$m = \frac{3}{4}$

$b = \frac{5}{4}$

Step 2.2

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

Slope: $\frac{3}{4}$

y-intercept: $(0, \frac{5}{4})$

Slope: $\frac{3}{4}$

y-intercept: $(0, \frac{5}{4})$

Step 3

Graph a dashed line, then shade the area below the boundary line since $y$ is less than $\frac{3}{4} x + \frac{5}{4}$ .

$y < \frac{3}{4} x + \frac{5}{4}$

Step 4