Find the Slope of a Parallel Line 4x+8y=24

$4 x + 8 y = 24$

Step 1

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 $4 x$ from both sides of the equation.

$8 y = 24 - 4 x$

Divide each term in $8 y = 24 - 4 x$ by $8$ and simplify.

Divide each term in $8 y = 24 - 4 x$ by $8$ .

$\frac{8 y}{8} = \frac{24}{8} + \frac{- 4 x}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{24}{8} + \frac{- 4 x}{8}$

Divide $y$ by $1$ .

$y = \frac{24}{8} + \frac{- 4 x}{8}$

Simplify the right side.

Simplify each term.

Divide $24$ by $8$ .

$y = 3 + \frac{- 4 x}{8}$

Cancel the common factor of $- 4$ and $8$ .

Factor $4$ out of $- 4 x$ .

$y = 3 + \frac{4 (- x)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

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

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

Reorder terms.

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

Remove parentheses.

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

Step 2

Using the slope-intercept form, the slope is $- \frac{1}{2}$ .

$m = - \frac{1}{2}$

Step 3

All lines that are parallel to $y = - \frac{1}{2} x + 3$ have the same slope of $- \frac{1}{2}$ .

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

Step 4

Find the Slope of a Parallel Line 4x+8y=24

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