Find the Parallel Line (-1,-2) , 3x-y=5

$(- 1, - 2)$ , $3 x - y = 5$

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 $3 x$ from both sides of the equation.

$- y = 5 - 3 x$

Divide each term in $- y = 5 - 3 x$ by $- 1$ and simplify.

Divide each term in $- y = 5 - 3 x$ by $- 1$ .

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Divide $5$ by $- 1$ .

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

Move the negative one from the denominator of $\frac{- 3 x}{- 1}$ .

$y = - 5 - 1 \cdot (- 3 x)$

Rewrite $- 1 \cdot (- 3 x)$ as $- (- 3 x)$ .

$y = - 5 - (- 3 x)$

Multiply $- 3$ by $- 1$ .

$y = - 5 + 3 x$

Reorder $- 5$ and $3 x$ .

$y = 3 x - 5$

Step 2

Using the slope-intercept form, the slope is $3$ .

$m = 3$

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

$y - (- 2) = 3 \cdot (x - (- 1))$

Step 5

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

$y + 2 = 3 \cdot (x + 1)$

Step 6

Solve for $y$ .

Simplify $3 \cdot (x + 1)$ .

Rewrite.

$y + 2 = 0 + 0 + 3 \cdot (x + 1)$

Simplify by adding zeros.

$y + 2 = 3 \cdot (x + 1)$

Apply the distributive property.

$y + 2 = 3 x + 3 \cdot 1$

Multiply $3$ by $1$ .

$y + 2 = 3 x + 3$

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

Subtract $2$ from both sides of the equation.

$y = 3 x + 3 - 2$

Subtract $2$ from $3$ .

$y = 3 x + 1$

Step 7

Find the Parallel Line (-1,-2) , 3x-y=5

Related Questions

Support LCMGCF.com by disabling your adblocker.