Finite Math Examples

$p = 4 x + 6 y$

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

Rewrite the equation as $4 x + 6 y = p$ .

$4 x + 6 y = p$

Step 1.3

Subtract $4 x$ from both sides of the equation.

$6 y = p - 4 x$

Step 1.4

Divide each term in $6 y = p - 4 x$ by $6$ and simplify.

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Step 1.4.1

Divide each term in $6 y = p - 4 x$ by $6$ .

$\frac{6 y}{6} = \frac{p}{6} + \frac{- 4 x}{6}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $6$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{p}{6} + \frac{- 4 x}{6}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{p}{6} + \frac{- 4 x}{6}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Cancel the common factor of $- 4$ and $6$ .

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Step 1.4.3.1.1.1

Factor $2$ out of $- 4 x$ .

$y = \frac{p}{6} + \frac{2 (- 2 x)}{6}$

Step 1.4.3.1.1.2

Cancel the common factors.

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Step 1.4.3.1.1.2.1

Factor $2$ out of $6$ .

$y = \frac{p}{6} + \frac{2 (- 2 x)}{2 (3)}$

Step 1.4.3.1.1.2.2

Cancel the common factor.

$y = \frac{p}{6} + \frac{2 (- 2 x)}{2 \cdot 3}$

Step 1.4.3.1.1.2.3

Rewrite the expression.

$y = \frac{p}{6} + \frac{- 2 x}{3}$

Step 1.4.3.1.2

Move the negative in front of the fraction.

$y = \frac{p}{6} - \frac{2 x}{3}$

Step 1.5

Rewrite in slope-intercept form.

$y = \frac{1}{6} p - \frac{2 x}{3}$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{1}{6}$

$b = - \frac{2 x}{3}$

Step 2.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{1}{6}$

y-intercept: $(0, - \frac{2 x}{3})$

Slope: $\frac{1}{6}$

y-intercept: $(0, - \frac{2 x}{3})$

Step 3