Write in Slope-Intercept Form

$3 x + 4 y = - 5$

Step 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

Rewrite in slope-intercept form.

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Step 2.1

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

$4 y = - 5 - 3 x$

Step 2.2

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

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Step 2.2.1

Divide each term in $4 y = - 5 - 3 x$ by $4$ .

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

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $4$ .

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Step 2.2.2.1.1

Cancel the common factor.

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

Step 2.2.2.1.2

Divide $y$ by $1$ .

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

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Move the negative in front of the fraction.

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

Step 2.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{5}{4} - \frac{3 x}{4}$

Step 2.3

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

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Step 2.3.1

Reorder $- \frac{5}{4}$ and $- \frac{3 x}{4}$ .

$y = - \frac{3 x}{4} - \frac{5}{4}$

Step 2.3.2

Reorder terms.

$y = - (\frac{3}{4} x) - \frac{5}{4}$

Step 2.3.3

Remove parentheses.

$y = - \frac{3}{4} x - \frac{5}{4}$

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