Finite Math Examples

$y = \frac{4}{3} x - 7$ , $(1, 3)$

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

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

$y = \frac{4 x}{3} - 7$

Step 1.3

Reorder terms.

$y = \frac{4}{3} x - 7$

Step 2

Using the slope-intercept form, the slope is $\frac{4}{3}$ .

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

Step 3

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Step 4

Use the slope $\frac{4}{3}$ and a given point $(1, 3)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Step 5

Simplify the equation and keep it in point-slope form.

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

Step 6

Solve for $y$ .

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Step 6.1

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

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Step 6.1.1

Rewrite.

$y - 3 = 0 + 0 + \frac{4}{3} \cdot (x - 1)$

Step 6.1.2

Simplify by adding zeros.

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

Step 6.1.3

Apply the distributive property.

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

Step 6.1.4

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

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

Step 6.1.5

Multiply $\frac{4}{3} \cdot - 1$ .

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Step 6.1.5.1

Combine $\frac{4}{3}$ and $- 1$ .

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

Step 6.1.5.2

Multiply $4$ by $- 1$ .

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

Step 6.1.6

Move the negative in front of the fraction.

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

Step 6.2

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

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Step 6.2.1

Add $3$ to both sides of the equation.

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

Step 6.2.2

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

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

Step 6.2.3

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

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

Step 6.2.4

Combine the numerators over the common denominator.

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

Step 6.2.5

Simplify the numerator.

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Step 6.2.5.1

Multiply $3$ by $3$ .

$y = \frac{4 x}{3} + \frac{- 4 + 9}{3}$

Step 6.2.5.2

Add $- 4$ and $9$ .

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

Step 6.3

Reorder terms.

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

Step 7