Finite Math Examples

$\frac{x}{3} + \frac{y}{4} = 1$

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 $\frac{x}{3}$ from both sides of the equation.

$\frac{y}{4} = 1 - \frac{x}{3}$

Step 1.3

Multiply both sides of the equation by $4$ .

$4 \frac{y}{4} = 4 (1 - \frac{x}{3})$

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Cancel the common factor of $4$ .

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Step 1.4.1.1.1

Cancel the common factor.

$4 \frac{y}{4} = 4 (1 - \frac{x}{3})$

Step 1.4.1.1.2

Rewrite the expression.

$y = 4 (1 - \frac{x}{3})$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $4 (1 - \frac{x}{3})$ .

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Step 1.4.2.1.1

Apply the distributive property.

$y = 4 \cdot 1 + 4 (- \frac{x}{3})$

Step 1.4.2.1.2

Multiply $4$ by $1$ .

$y = 4 + 4 (- \frac{x}{3})$

Step 1.4.2.1.3

Multiply $4 (- \frac{x}{3})$ .

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Step 1.4.2.1.3.1

Multiply $- 1$ by $4$ .

$y = 4 - 4 \frac{x}{3}$

Step 1.4.2.1.3.2

Combine $- 4$ and $\frac{x}{3}$ .

$y = 4 + \frac{- 4 x}{3}$

Step 1.4.2.1.4

Move the negative in front of the fraction.

$y = 4 - \frac{4 x}{3}$

Step 1.5

Reorder $4$ and $- \frac{4 x}{3}$ .

$y = - \frac{4 x}{3} + 4$

Step 1.6

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

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Step 1.6.1

Reorder terms.

$y = - (\frac{4}{3} x) + 4$

Step 1.6.2

Remove parentheses.

$y = - \frac{4}{3} x + 4$

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 $y = m x + b$ .

$m = - \frac{4}{3}$

$b = 4$

Step 2.2

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

Slope: $- \frac{4}{3}$

y-intercept: $(0, 4)$

Slope: $- \frac{4}{3}$

y-intercept: $(0, 4)$

Step 3