Determine if Parallel y=5x+6 -18x+3y=-54

$y = 5 x + 6$ $- 18 x + 3 y = - 54$

Use the slope-intercept form to find the slope and y-intercept.

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

$y = m x + b$

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

$m_{1} = 5$

$b = 6$

$m_{1} = 5$

$b = 6$

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.

$y = m x + b$

Add $18 x$ to both sides of the equation.

$3 y = - 54 + 18 x$

Divide each term in $3 y = - 54 + 18 x$ by $3$ and simplify.

Divide each term in $3 y = - 54 + 18 x$ by $3$ .

$\frac{3 y}{3} = \frac{- 54}{3} + \frac{18 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 54}{3} + \frac{18 x}{3}$

Divide $y$ by $1$ .

$y = \frac{- 54}{3} + \frac{18 x}{3}$

Simplify the right side.

Simplify each term.

Divide $- 54$ by $3$ .

$y = - 18 + \frac{18 x}{3}$

Cancel the common factor of $18$ and $3$ .

Factor $3$ out of $18 x$ .

$y = - 18 + \frac{3 (6 x)}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$y = - 18 + \frac{3 (6 x)}{3 (1)}$

Cancel the common factor.

$y = - 18 + \frac{3 (6 x)}{3 \cdot 1}$

Rewrite the expression.

$y = - 18 + \frac{6 x}{1}$

Divide $6 x$ by $1$ .

$y = - 18 + 6 x$

Reorder $- 18$ and $6 x$ .

$y = 6 x - 18$

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

$m_{2} = 6$

$b = - 18$

$m_{2} = 6$

$b = - 18$

Compare the slopes $m$ of the two equations.

$m_{1} = 5, m_{2} = 6$

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.

$m_{1} = 5, m_{2} = 6$

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

Not Parallel

Determine if Parallel y=5x+6 -18x+3y=-54

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