Precalculus Examples

$a x + b y = c$

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 $a x$ from both sides of the equation.

$b y = c - a x$

Step 1.3

Divide each term in $b y = c - a x$ by $b$ and simplify.

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Step 1.3.1

Divide each term in $b y = c - a x$ by $b$ .

$\frac{b y}{b} = \frac{c}{b} + \frac{- a x}{b}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $b$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{b y}{b} = \frac{c}{b} + \frac{- a x}{b}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{c}{b} + \frac{- a x}{b}$

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.

$y = \frac{c}{b} - \frac{a x}{b}$

Step 1.4

Rewrite in slope-intercept form.

$y = \frac{1}{b} c - \frac{a x}{b}$

Step 2

The equation is not linear, so a constant slope does not exist.

Not Linear