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

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

Choose a point that the parallel line will pass through.

$(0, 0)$

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 each term.

Combine $x$ and $\frac{2}{3}$ .

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

Move $2$ to the left of $x$ .

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

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

Reorder terms.

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

Remove parentheses.

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

Using the slope-intercept form, the slope is $- \frac{2}{3}$ .

$m = - \frac{2}{3}$

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

Use the slope $- \frac{2}{3}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{2}{3} \cdot (x - (0))$

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

$y + 0 = - \frac{2}{3} \cdot (x + 0)$

Solve for $y$ .

Add $y$ and $0$ .

$y = - \frac{2}{3} \cdot (x + 0)$

Simplify $- \frac{2}{3} \cdot (x + 0)$ .

Add $x$ and $0$ .

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

Combine $x$ and $\frac{2}{3}$ .

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

Move $2$ to the left of $x$ .

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

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

Reorder terms.

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

Remove parentheses.

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

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

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