Algebra Examples

$3 x + 5 y = - 7$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

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

$5 y = - 7 - 3 x$

Step 1.3

Divide each term in $5 y = - 7 - 3 x$ by $5$ and simplify.

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Step 1.3.1

Divide each term in $5 y = - 7 - 3 x$ by $5$ .

$\frac{5 y}{5} = \frac{- 7}{5} + \frac{- 3 x}{5}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $5$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 7}{5} + \frac{- 3 x}{5}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 7}{5} + \frac{- 3 x}{5}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Move the negative in front of the fraction.

$y = - \frac{7}{5} + \frac{- 3 x}{5}$

Step 1.3.3.1.2

Move the negative in front of the fraction.

$y = - \frac{7}{5} - \frac{3 x}{5}$

Step 1.4

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

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Step 1.4.1

Reorder $- \frac{7}{5}$ and $- \frac{3 x}{5}$ .

$y = - \frac{3 x}{5} - \frac{7}{5}$

Step 1.4.2

Reorder terms.

$y = - (\frac{3}{5} x) - \frac{7}{5}$

Step 1.4.3

Remove parentheses.

$y = - \frac{3}{5} x - \frac{7}{5}$

Step 2

Using the slope-intercept form, the slope is $- \frac{3}{5}$ .

$m = - \frac{3}{5}$

Step 3