Finite Math Examples

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

Step 1

Choose a point that the parallel line will pass through.

$(0, 0)$

Step 2

Rewrite in slope-intercept form.

Tap for more steps...

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

Simplify the left side.

Tap for more steps...

Step 2.2.1

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

Tap for more steps...

Step 2.2.1.1

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

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

Step 2.2.1.2

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

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

Step 2.3

Rewrite the equation as $3 y - 2 = - \frac{3 x}{5}$ .

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

Step 2.4

Add $2$ to both sides of the equation.

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

Step 2.5

Divide each term in $3 y = - \frac{3 x}{5} + 2$ by $3$ and simplify.

Tap for more steps...

Step 2.5.1

Divide each term in $3 y = - \frac{3 x}{5} + 2$ by $3$ .

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

Step 2.5.2

Simplify the left side.

Tap for more steps...

Step 2.5.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.5.2.1.1

Cancel the common factor.

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

Step 2.5.2.1.2

Divide $y$ by $1$ .

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

Step 2.5.3

Simplify the right side.

Tap for more steps...

Step 2.5.3.1

Simplify each term.

Tap for more steps...

Step 2.5.3.1.1

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{3 x}{5} \cdot \frac{1}{3} + \frac{2}{3}$

Step 2.5.3.1.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.5.3.1.2.1

Move the leading negative in $- \frac{3 x}{5}$ into the numerator.

$y = \frac{- 3 x}{5} \cdot \frac{1}{3} + \frac{2}{3}$

Step 2.5.3.1.2.2

Factor $3$ out of $- 3 x$ .

$y = \frac{3 (- x)}{5} \cdot \frac{1}{3} + \frac{2}{3}$

Step 2.5.3.1.2.3

Cancel the common factor.

$y = \frac{3 (- x)}{5} \cdot \frac{1}{3} + \frac{2}{3}$

Step 2.5.3.1.2.4

Rewrite the expression.

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

Step 2.5.3.1.3

Move the negative in front of the fraction.

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

Step 2.6

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

Tap for more steps...

Step 2.6.1

Reorder terms.

$y = - (\frac{1}{5} x) + \frac{2}{3}$

Step 2.6.2

Remove parentheses.

$y = - \frac{1}{5} x + \frac{2}{3}$

Step 3

Using the slope-intercept form, the slope is $- \frac{1}{5}$ .

$m = - \frac{1}{5}$

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

$y - (0) = - \frac{1}{5} \cdot (x - (0))$

Step 6

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

$y + 0 = - \frac{1}{5} \cdot (x + 0)$

Step 7

Solve for $y$ .

Tap for more steps...

Step 7.1

Add $y$ and $0$ .

$y = - \frac{1}{5} \cdot (x + 0)$

Step 7.2

Simplify $- \frac{1}{5} \cdot (x + 0)$ .

Tap for more steps...

Step 7.2.1

Add $x$ and $0$ .

$y = - \frac{1}{5} \cdot x$

Step 7.2.2

Combine $x$ and $\frac{1}{5}$ .

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

Step 7.3

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

Tap for more steps...

Step 7.3.1

Reorder terms.

$y = - (\frac{1}{5} x)$

Step 7.3.2

Remove parentheses.

$y = - \frac{1}{5} x$

Step 8