Find the Parallel Line (-1,6) and parallel to x+3y=5

$(- 1, 6)$ and parallel to $x + 3 y = 5$

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.

$3 y = 5 - x$

Divide each term in $3 y = 5 - x$ by $3$ and simplify.

Divide each term in $3 y = 5 - x$ by $3$ .

$\frac{3 y}{3} = \frac{5}{3} + \frac{- x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{5}{3} + \frac{- x}{3}$

Divide $y$ by $1$ .

$y = \frac{5}{3} + \frac{- x}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{5}{3} - \frac{x}{3}$

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

Reorder $\frac{5}{3}$ and $- \frac{x}{3}$ .

$y = - \frac{x}{3} + \frac{5}{3}$

Reorder terms.

$y = - (\frac{1}{3} x) + \frac{5}{3}$

Remove parentheses.

$y = - \frac{1}{3} x + \frac{5}{3}$

Using the slope-intercept form, the slope is $- \frac{1}{3}$ .

$m = - \frac{1}{3}$

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

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

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

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

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

Solve for $y$ .

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

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Combine $x$ and $\frac{1}{3}$ .

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

Multiply $- 1$ by $1$ .

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

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

Add $6$ to both sides of the equation.

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

To write $6$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Combine $6$ and $\frac{3}{3}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $6$ by $3$ .

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

Add $- 1$ and $18$ .

$y = - \frac{x}{3} + \frac{17}{3}$

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

Reorder terms.

$y = - (\frac{1}{3} x) + \frac{17}{3}$

Remove parentheses.

$y = - \frac{1}{3} x + \frac{17}{3}$

Find the Parallel Line (-1,6) and parallel to x+3y=5

Related Questions

Support LCMGCF.com by disabling your adblocker.