Finite Math Examples

$3 x + 7 y = 0$

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

Subtract $3 x$ from both sides of the equation.

$7 y = - 3 x$

Step 2.3

Divide each term in $7 y = - 3 x$ by $7$ and simplify.

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Step 2.3.1

Divide each term in $7 y = - 3 x$ by $7$ .

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $7$ .

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Step 2.3.2.1.1

Cancel the common factor.

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

Step 2.3.2.1.2

Divide $y$ by $1$ .

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

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

Step 2.4

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

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Step 2.4.1

Reorder terms.

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

Step 2.4.2

Remove parentheses.

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

Step 3

Using the slope-intercept form, the slope is $- \frac{3}{7}$ .

$m = - \frac{3}{7}$

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 $- \frac{3}{7}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{3}{7} \cdot (x - (1))$

Step 6

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

$y + 0 = - \frac{3}{7} \cdot (x - 1)$

Step 7

Solve for $y$ .

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Step 7.1

Add $y$ and $0$ .

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

Step 7.2

Simplify $- \frac{3}{7} \cdot (x - 1)$ .

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Step 7.2.1

Apply the distributive property.

$y = - \frac{3}{7} x - \frac{3}{7} \cdot - 1$

Step 7.2.2

Combine $x$ and $\frac{3}{7}$ .

$y = - \frac{x \cdot 3}{7} - \frac{3}{7} \cdot - 1$

Step 7.2.3

Multiply $- \frac{3}{7} \cdot - 1$ .

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Step 7.2.3.1

Multiply $- 1$ by $- 1$ .

$y = - \frac{x \cdot 3}{7} + 1 (\frac{3}{7})$

Step 7.2.3.2

Multiply $\frac{3}{7}$ by $1$ .

$y = - \frac{x \cdot 3}{7} + \frac{3}{7}$

Step 7.2.4

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

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

Step 7.3

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

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Step 7.3.1

Reorder terms.

$y = - (\frac{3}{7} x) + \frac{3}{7}$

Step 7.3.2

Remove parentheses.

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

Step 8