Determine if Parallel 3x+2y=8 2x+3y=-12

$3 x + 2 y = 8$ $2 x + 3 y = - 12$

Step 1

Find the slope and y-intercept of the first equation.

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.

$y = m x + b$

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

$2 y = 8 - 3 x$

Divide each term in $2 y = 8 - 3 x$ by $2$ and simplify.

Divide each term in $2 y = 8 - 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{8}{2} + \frac{- 3 x}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y}{2} = \frac{8}{2} + \frac{- 3 x}{2}$

Divide $y$ by $1$ .

$y = \frac{8}{2} + \frac{- 3 x}{2}$

Simplify the right side.

Simplify each term.

Divide $8$ by $2$ .

$y = 4 + \frac{- 3 x}{2}$

Move the negative in front of the fraction.

$y = 4 - \frac{3 x}{2}$

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

Reorder $4$ and $- \frac{3 x}{2}$ .

$y = - \frac{3 x}{2} + 4$

Reorder terms.

$y = - (\frac{3}{2} x) + 4$

Remove parentheses.

$y = - \frac{3}{2} x + 4$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m_{1} = - \frac{3}{2}$

$b = 4$

$m_{1} = - \frac{3}{2}$

$b = 4$

Step 2

Find the slope and y-intercept of the second equation.

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.

$y = m x + b$

Subtract $2 x$ from both sides of the equation.

$3 y = - 12 - 2 x$

Divide each term in $3 y = - 12 - 2 x$ by $3$ and simplify.

Divide each term in $3 y = - 12 - 2 x$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $- 12$ by $3$ .

$y = - 4 + \frac{- 2 x}{3}$

Move the negative in front of the fraction.

$y = - 4 - \frac{2 x}{3}$

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

Reorder $- 4$ and $- \frac{2 x}{3}$ .

$y = - \frac{2 x}{3} - 4$

Reorder terms.

$y = - (\frac{2}{3} x) - 4$

Remove parentheses.

$y = - \frac{2}{3} x - 4$

Find the values of $m$ and $b$ using the form $y = m x + b$ .

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

$b = - 4$

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

$b = - 4$

Step 3

Compare the slopes $m$ of the two equations.

$m_{1} = - \frac{3}{2}, m_{2} = - \frac{2}{3}$

Step 4

Compare the two slopes in the decimal form. If the slopes are equal, then the lines are parallel. If the slopes are not equal, then the lines are not parallel.

$m_{1} = - 1.5, m_{2} = - 0.\overline{6}$

Step 5

The equations are not parallel because the slopes of the two lines are not equal.

Not Parallel

Step 6

Determine if Parallel 3x+2y=8 2x+3y=-12

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