Determine if Parallel 2x=-1-y , 2y=6x+5

$2 x = - 1 - y$ , $2 y = 6 x + 5$

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

Tap for more steps…

Rewrite in slope-intercept form.

Tap for more steps…

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

$y = m x + b$

Rewrite the equation as $- 1 - y = 2 x$ .

$- 1 - y = 2 x$

Add $1$ to both sides of the equation.

$- y = 2 x + 1$

Multiply each term in $- y = 2 x + 1$ by $- 1$

Tap for more steps…

Multiply each term in $- y = 2 x + 1$ by $- 1$ .

$(- y) \cdot - 1 = 2 x \cdot - 1 + 1 \cdot - 1$

Multiply $(- y) \cdot - 1$ .

Tap for more steps…

Multiply $- 1$ by $- 1$ .

$1 y = 2 x \cdot - 1 + 1 \cdot - 1$

Multiply $y$ by $1$ .

$y = 2 x \cdot - 1 + 1 \cdot - 1$

Simplify each term.

Tap for more steps…

Multiply $- 1$ by $2$ .

$y = - 2 x + 1 \cdot - 1$

Multiply $- 1$ by $1$ .

$y = - 2 x - 1$

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

$m_{1} = - 2$

$b = - 1$

$m_{1} = - 2$

$b = - 1$

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

Tap for more steps…

Rewrite in slope-intercept form.

Tap for more steps…

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 by $2$ and simplify.

Tap for more steps…

Divide each term in $2 y = 6 x + 5$ by $2$ .

$\frac{2 y}{2} = \frac{6 x}{2} + \frac{5}{2}$

Cancel the common factor of $2$ .

Tap for more steps…

Cancel the common factor.

$\frac{2 y}{2} = \frac{6 x}{2} + \frac{5}{2}$

Divide $y$ by $1$ .

$y = \frac{6 x}{2} + \frac{5}{2}$

Cancel the common factor of $6$ and $2$ .

Tap for more steps…

Factor $2$ out of $6 x$ .

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

Cancel the common factors.

Tap for more steps…

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3 x$ by $1$ .

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

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

$m_{2} = 3$

$b = \frac{5}{2}$

$m_{2} = 3$

$b = \frac{5}{2}$

Compare the slopes $m$ of the two equations.

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

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.

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

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

Not Parallel

Determine if Parallel 2x=-1-y , 2y=6x+5