Determine if Parallel 3y=4x+15 and 9x+12y=12

$3 y = 4 x + 15$ and $9 x + 12 y = 12$

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.

$y = m x + b$

Divide each term in $3 y = 4 x + 15$ by $3$ and simplify.

Divide each term in $3 y = 4 x + 15$ by $3$ .

$\frac{3 y}{3} = \frac{4 x}{3} + \frac{15}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{4 x}{3} + \frac{15}{3}$

Divide $y$ by $1$ .

$y = \frac{4 x}{3} + \frac{15}{3}$

Simplify the right side.

Divide $15$ by $3$ .

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

Reorder terms.

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

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

$m_{1} = \frac{4}{3}$

$b = 5$

$m_{1} = \frac{4}{3}$

$b = 5$

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 $9 x$ from both sides of the equation.

$12 y = 12 - 9 x$

Divide each term in $12 y = 12 - 9 x$ by $12$ and simplify.

Divide each term in $12 y = 12 - 9 x$ by $12$ .

$\frac{12 y}{12} = \frac{12}{12} + \frac{- 9 x}{12}$

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12 y}{12} = \frac{12}{12} + \frac{- 9 x}{12}$

Divide $y$ by $1$ .

$y = \frac{12}{12} + \frac{- 9 x}{12}$

Simplify the right side.

Simplify each term.

Divide $12$ by $12$ .

$y = 1 + \frac{- 9 x}{12}$

Cancel the common factor of $- 9$ and $12$ .

Factor $3$ out of $- 9 x$ .

$y = 1 + \frac{3 (- 3 x)}{12}$

Cancel the common factors.

Factor $3$ out of $12$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

Reorder $1$ and $- \frac{3 x}{4}$ .

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

Reorder terms.

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

Remove parentheses.

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

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

$m_{2} = - \frac{3}{4}$

$b = 1$

$m_{2} = - \frac{3}{4}$

$b = 1$

Step 3

Compare the slopes $m$ of the two equations.

$m_{1} = \frac{4}{3}, m_{2} = - \frac{3}{4}$

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.

$m_{1} = 1.\overline{3}, m_{2} = - 0.75$

Step 5

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

Not Parallel

Step 6

Determine if Parallel 3y=4x+15 and 9x+12y=12

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