Find the Parallel Line (-3,6) x+2y=5

$(- 3, 6)$ $x + 2 y = 5$

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 $x$ from both sides of the equation.

$2 y = 5 - x$

Divide each term in $2 y = 5 - x$ by $2$ and simplify.

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

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

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

Reorder terms.

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

Remove parentheses.

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

Step 2

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

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

Step 3

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

Step 4

Use the slope $- \frac{1}{2}$ and a given point $(- 3, 6)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (6) = - \frac{1}{2} \cdot (x - (- 3))$

Step 5

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

$y - 6 = - \frac{1}{2} \cdot (x + 3)$

Step 6

Solve for $y$ .

Simplify $- \frac{1}{2} \cdot (x + 3)$ .

Rewrite.

$y - 6 = 0 + 0 - \frac{1}{2} \cdot (x + 3)$

Simplify by adding zeros.

$y - 6 = - \frac{1}{2} \cdot (x + 3)$

Apply the distributive property.

$y - 6 = - \frac{1}{2} x - \frac{1}{2} \cdot 3$

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

$y - 6 = - \frac{x}{2} - \frac{1}{2} \cdot 3$

Multiply $- \frac{1}{2} \cdot 3$ .

Multiply $3$ by $- 1$ .

$y - 6 = - \frac{x}{2} - 3 (\frac{1}{2})$

Combine $- 3$ and $\frac{1}{2}$ .

$y - 6 = - \frac{x}{2} + \frac{- 3}{2}$

Move the negative in front of the fraction.

$y - 6 = - \frac{x}{2} - \frac{3}{2}$

Move all terms not containing $y$ to the right side of the equation.

Add $6$ to both sides of the equation.

$y = - \frac{x}{2} - \frac{3}{2} + 6$

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{x}{2} - \frac{3}{2} + 6 \cdot \frac{2}{2}$

Combine $6$ and $\frac{2}{2}$ .

$y = - \frac{x}{2} - \frac{3}{2} + \frac{6 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = - \frac{x}{2} + \frac{- 3 + 6 \cdot 2}{2}$

Simplify the numerator.

Multiply $6$ by $2$ .

$y = - \frac{x}{2} + \frac{- 3 + 12}{2}$

Add $- 3$ and $12$ .

$y = - \frac{x}{2} + \frac{9}{2}$

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

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{9}{2}$

Remove parentheses.

$y = - \frac{1}{2} x + \frac{9}{2}$

Step 7

Find the Parallel Line (-3,6) x+2y=5

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