Finite Math Examples

$3 x = 4 y + 5$

Step 1

Choose a point that the parallel line will pass through.

$(0, 0)$

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

Rewrite the equation as $4 y + 5 = 3 x$ .

$4 y + 5 = 3 x$

Step 2.3

Subtract $5$ from both sides of the equation.

$4 y = 3 x - 5$

Step 2.4

Divide each term in $4 y = 3 x - 5$ by $4$ and simplify.

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Step 2.4.1

Divide each term in $4 y = 3 x - 5$ by $4$ .

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

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $4$ .

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Step 2.4.2.1.1

Cancel the common factor.

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

Step 2.4.2.1.2

Divide $y$ by $1$ .

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

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Move the negative in front of the fraction.

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

Step 2.5

Reorder terms.

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

Step 3

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

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

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 $\frac{3}{4}$ and a given point $(0, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Step 6

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

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

Step 7

Solve for $y$ .

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Step 7.1

Add $y$ and $0$ .

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

Step 7.2

Simplify $\frac{3}{4} \cdot (x + 0)$ .

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Step 7.2.1

Add $x$ and $0$ .

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

Step 7.2.2

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

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

Step 7.3

Reorder terms.

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

Step 8