Finite Math Examples Linear Functions and Points

Find the Parallel Line

$y = 3 x - 21$ , $(- 7, 0)$

Step 1

Use the slope-intercept form to find the slope.

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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

Using the slope-intercept form, the slope is $3$ .

$m = 3$

Step 2

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

Step 3

Use the slope $3$ and a given point $(- 7, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = 3 \cdot (x - (- 7))$

Step 4

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

$y + 0 = 3 \cdot (x + 7)$

Step 5

Solve for $y$ .

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Step 5.1

Add $y$ and $0$ .

$y = 3 \cdot (x + 7)$

Step 5.2

Simplify $3 \cdot (x + 7)$ .

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Step 5.2.1

Apply the distributive property.

$y = 3 x + 3 \cdot 7$

Step 5.2.2

Multiply $3$ by $7$ .

$y = 3 x + 21$

Step 6

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Find the Parallel Line

Linear Functions and Points

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