Algebra Examples

$p x - q y = r$

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 $p x$ from both sides of the equation.

$- q y = r - p x$

Step 1.3

Divide each term in $- q y = r - p x$ by $- q$ and simplify.

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Step 1.3.1

Divide each term in $- q y = r - p x$ by $- q$ .

$\frac{- q y}{- q} = \frac{r}{- q} + \frac{- p x}{- q}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Dividing two negative values results in a positive value.

$\frac{q y}{q} = \frac{r}{- q} + \frac{- p x}{- q}$

Step 1.3.2.2

Cancel the common factor of $q$ .

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Step 1.3.2.2.1

Cancel the common factor.

$\frac{q y}{q} = \frac{r}{- q} + \frac{- p x}{- q}$

Step 1.3.2.2.2

Divide $y$ by $1$ .

$y = \frac{r}{- q} + \frac{- p x}{- q}$

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.

$y = - \frac{r}{q} + \frac{- p x}{- q}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

$y = - \frac{r}{q} + \frac{p x}{q}$

Step 1.4

Rewrite in slope-intercept form.

$y = - \frac{1}{q} r + \frac{p x}{q}$

Step 2

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

Not Linear