Precalculus Examples

$(0, 1)$ , $3 x + 4 y + 5 = 0$

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

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

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Step 1.2.1

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

$4 y + 5 = - 3 x$

Step 1.2.2

Subtract $5$ from both sides of the equation.

$4 y = - 3 x - 5$

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide $y$ by $1$ .

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

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Move the negative in front of the fraction.

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

Step 1.3.3.1.2

Move the negative in front of the fraction.

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

Step 1.4

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

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Step 1.4.1

Reorder terms.

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

Step 1.4.2

Remove parentheses.

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

Step 2

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

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

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

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

Step 5

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

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

Step 6

Solve for $y$ .

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Step 6.1

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

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Step 6.1.1

Add $x$ and $0$ .

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

Step 6.1.2

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

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

Step 6.1.3

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

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

Step 6.2

Add $1$ to both sides of the equation.

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

Step 6.3

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

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Step 6.3.1

Reorder terms.

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

Step 6.3.2

Remove parentheses.

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

Step 7