Find the Parallel Line What is an equation of the line that passes through the point (-8,0) and is parallel to the line x-2y=10 ?

What is an equation of the line that passes through the point $(- 8, 0)$ and is parallel to the line $x - 2 y = 10$ ?

Write the problem as a mathematical expression.

$(- 8, 0)$ , $x - 2 y = 10$

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 $x$ from both sides of the equation.

$- 2 y = 10 - x$

Divide each term in $- 2 y = 10 - x$ by $- 2$ and simplify.

Divide each term in $- 2 y = 10 - x$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- x}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{10}{- 2} + \frac{- x}{- 2}$

Divide $y$ by $1$ .

$y = \frac{10}{- 2} + \frac{- x}{- 2}$

Simplify the right side.

Simplify each term.

Divide $10$ by $- 2$ .

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

Dividing two negative values results in a positive value.

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

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

Reorder $- 5$ and $\frac{x}{2}$ .

$y = \frac{x}{2} - 5$

Reorder terms.

$y = \frac{1}{2} x - 5$

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

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

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Use the slope $\frac{1}{2}$ and a given point $(- 8, 0)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = \frac{1}{2} \cdot (x - (- 8))$

Simplify the equation and keep it in point-slope form.

$y + 0 = \frac{1}{2} \cdot (x + 8)$

Solve for $y$ .

Add $y$ and $0$ .

$y = \frac{1}{2} \cdot (x + 8)$

Simplify $\frac{1}{2} \cdot (x + 8)$ .

Apply the distributive property.

$y = \frac{1}{2} x + \frac{1}{2} \cdot 8$

Combine $\frac{1}{2}$ and $x$ .

$y = \frac{x}{2} + \frac{1}{2} \cdot 8$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$y = \frac{x}{2} + \frac{1}{2} \cdot (2 (4))$

Cancel the common factor.

$y = \frac{x}{2} + \frac{1}{2} \cdot (2 \cdot 4)$

Rewrite the expression.

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

Reorder terms.

$y = \frac{1}{2} x + 4$

Find the Parallel Line What is an equation of the line that passes through the point (-8,0) and is parallel to the line x-2y=10 ?

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