Finite Math Examples

$y - 0 = \frac{4}{5} \cdot (x - 0)$

Step 1

Choose a point that the parallel line will pass through.

$(1, 0)$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

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 2.2

Simplify the left side.

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Step 2.2.1

Subtract $0$ from $y$ .

$y = \frac{4}{5} \cdot (x - 0)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify $\frac{4}{5} \cdot (x - 0)$ .

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Step 2.3.1.1

Subtract $0$ from $x$ .

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

Step 2.3.1.2

Combine $\frac{4}{5}$ and $x$ .

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

Step 2.4

Reorder terms.

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

Step 3

Using the slope-intercept form, the slope is $\frac{4}{5}$ .

$m = \frac{4}{5}$

Step 4

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

Step 5

Use the slope $\frac{4}{5}$ and a given point $(1, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = \frac{4}{5} \cdot (x - (1))$

Step 6

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

$y + 0 = \frac{4}{5} \cdot (x - 1)$

Step 7

Solve for $y$ .

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Step 7.1

Add $y$ and $0$ .

$y = \frac{4}{5} \cdot (x - 1)$

Step 7.2

Simplify $\frac{4}{5} \cdot (x - 1)$ .

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Step 7.2.1

Apply the distributive property.

$y = \frac{4}{5} x + \frac{4}{5} \cdot - 1$

Step 7.2.2

Combine $\frac{4}{5}$ and $x$ .

$y = \frac{4 x}{5} + \frac{4}{5} \cdot - 1$

Step 7.2.3

Multiply $\frac{4}{5} \cdot - 1$ .

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Step 7.2.3.1

Combine $\frac{4}{5}$ and $- 1$ .

$y = \frac{4 x}{5} + \frac{4 \cdot - 1}{5}$

Step 7.2.3.2

Multiply $4$ by $- 1$ .

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

Step 7.2.4

Move the negative in front of the fraction.

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

Step 7.3

Reorder terms.

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

Step 8