Precalculus Examples

$3 x + 7 y + 13 = 5 + 3 x$

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

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

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Step 1.2.1

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

$7 y + 13 = 5 + 3 x - 3 x$

Step 1.2.2

Subtract $13$ from both sides of the equation.

$7 y = 5 + 3 x - 3 x - 13$

Step 1.2.3

Combine the opposite terms in $5 + 3 x - 3 x - 13$ .

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Step 1.2.3.1

Subtract $3 x$ from $3 x$ .

$7 y = 5 + 0 - 13$

Step 1.2.3.2

Add $5$ and $0$ .

$7 y = 5 - 13$

Step 1.2.4

Subtract $13$ from $5$ .

$7 y = - 8$

Step 1.3

Divide each term in $7 y = - 8$ by $7$ and simplify.

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Step 1.3.1

Divide each term in $7 y = - 8$ by $7$ .

$\frac{7 y}{7} = \frac{- 8}{7}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $7$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 8}{7}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 8}{7}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Move the negative in front of the fraction.

$y = - \frac{8}{7}$

Step 2

Using the slope-intercept form, the slope is $0$ .

$m = 0$

Step 3