Find Any Equation Parallel to the Line y=-5/3x-12 2/3

$y = - \frac{5}{3} x - 12 \frac{2}{3}$

Step 1

Choose a point that the parallel line will pass through.

$(0, 0)$

Step 2

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Simplify the right side.

Simplify $- \frac{5}{3} x - 12 \frac{2}{3}$ .

Convert $12 \frac{2}{3}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$y = - \frac{5}{3} x - (12 + \frac{2}{3})$

Add $12$ and $\frac{2}{3}$ .

To write $12$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{5}{3} x - (12 \cdot \frac{3}{3} + \frac{2}{3})$

Combine $12$ and $\frac{3}{3}$ .

$y = - \frac{5}{3} x - (\frac{12 \cdot 3}{3} + \frac{2}{3})$

Combine the numerators over the common denominator.

$y = - \frac{5}{3} x - \frac{12 \cdot 3 + 2}{3}$

Simplify the numerator.

Multiply $12$ by $3$ .

$y = - \frac{5}{3} x - \frac{36 + 2}{3}$

Add $36$ and $2$ .

$y = - \frac{5}{3} x - \frac{38}{3}$

Simplify each term.

Combine $x$ and $\frac{5}{3}$ .

$y = - \frac{x \cdot 5}{3} - \frac{38}{3}$

Move $5$ to the left of $x$ .

$y = - \frac{5 x}{3} - \frac{38}{3}$

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

Reorder terms.

$y = - (\frac{5}{3} x) - \frac{38}{3}$

Remove parentheses.

$y = - \frac{5}{3} x - \frac{38}{3}$

Step 3

Using the slope-intercept form, the slope is $- \frac{5}{3}$ .

$m = - \frac{5}{3}$

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 $- \frac{5}{3}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{5}{3} \cdot (x - (0))$

Step 6

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

$y + 0 = - \frac{5}{3} \cdot (x + 0)$

Step 7

Solve for $y$ .

Add $y$ and $0$ .

$y = - \frac{5}{3} \cdot (x + 0)$

Simplify $- \frac{5}{3} \cdot (x + 0)$ .

Add $x$ and $0$ .

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

Combine $x$ and $\frac{5}{3}$ .

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

Move $5$ to the left of $x$ .

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

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

Reorder terms.

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

Remove parentheses.

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

Step 8

Find Any Equation Parallel to the Line y=-5/3x-12 2/3

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