Finite Math Examples

$y - 3 = - \frac{3}{4} \cdot (x + 5)$

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

Simplify the right side.

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Step 1.2.1

Simplify $- \frac{3}{4} \cdot (x + 5)$ .

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Step 1.2.1.1

Apply the distributive property.

$y - 3 = - \frac{3}{4} x - \frac{3}{4} \cdot 5$

Step 1.2.1.2

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

$y - 3 = - \frac{x \cdot 3}{4} - \frac{3}{4} \cdot 5$

Step 1.2.1.3

Multiply $- \frac{3}{4} \cdot 5$ .

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Step 1.2.1.3.1

Multiply $5$ by $- 1$ .

$y - 3 = - \frac{x \cdot 3}{4} - 5 (\frac{3}{4})$

Step 1.2.1.3.2

Combine $- 5$ and $\frac{3}{4}$ .

$y - 3 = - \frac{x \cdot 3}{4} + \frac{- 5 \cdot 3}{4}$

Step 1.2.1.3.3

Multiply $- 5$ by $3$ .

$y - 3 = - \frac{x \cdot 3}{4} + \frac{- 15}{4}$

Step 1.2.1.4

Simplify each term.

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Step 1.2.1.4.1

Move $3$ to the left of $x$ .

$y - 3 = - \frac{3 \cdot x}{4} + \frac{- 15}{4}$

Step 1.2.1.4.2

Move the negative in front of the fraction.

$y - 3 = - \frac{3 x}{4} - \frac{15}{4}$

Step 1.3

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

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Step 1.3.1

Add $3$ to both sides of the equation.

$y = - \frac{3 x}{4} - \frac{15}{4} + 3$

Step 1.3.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{3 x}{4} - \frac{15}{4} + 3 \cdot \frac{4}{4}$

Step 1.3.3

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

$y = - \frac{3 x}{4} - \frac{15}{4} + \frac{3 \cdot 4}{4}$

Step 1.3.4

Combine the numerators over the common denominator.

$y = - \frac{3 x}{4} + \frac{- 15 + 3 \cdot 4}{4}$

Step 1.3.5

Simplify the numerator.

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Step 1.3.5.1

Multiply $3$ by $4$ .

$y = - \frac{3 x}{4} + \frac{- 15 + 12}{4}$

Step 1.3.5.2

Add $- 15$ and $12$ .

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

Step 1.3.6

Move the negative in front of the fraction.

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

Step 1.4

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

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Step 1.4.1

Reorder terms.

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

Step 1.4.2

Remove parentheses.

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

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 $y = m x + b$ .

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

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

Step 2.2

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

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

y-intercept: $(0, - \frac{3}{4})$

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

y-intercept: $(0, - \frac{3}{4})$

Step 3