Find the Parallel Line (-1,4) and parallel to x+2y=5

$(- 1, 4)$ and parallel to $x + 2 y = 5$

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.

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

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 $(- 1, 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

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

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

Solve for $y$ .

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

Rewrite.

$y - 4 = 0 + 0 - \frac{1}{2} \cdot (x + 1)$

Simplify by adding zeros.

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

Apply the distributive property.

$y - 4 = - \frac{1}{2} x - \frac{1}{2} \cdot 1$

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

$y - 4 = - \frac{x}{2} - \frac{1}{2} \cdot 1$

Multiply $- 1$ by $1$ .

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

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

Add $4$ to both sides of the equation.

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

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $4$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $2$ .

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

Add $- 1$ and $8$ .

$y = - \frac{x}{2} + \frac{7}{2}$

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

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{7}{2}$

Remove parentheses.

$y = - \frac{1}{2} x + \frac{7}{2}$

Find the Parallel Line (-1,4) and parallel to x+2y=5

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