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

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

Step 1

Use the slope-intercept form to find the slope.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Using the slope-intercept form, the slope is $- 5$ .

$m = - 5$

Step 2

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

Step 3

Use the slope $- 5$ and a given point $(- 6, 3)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (3) = - 5 \cdot (x - (- 6))$

Step 4

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

$y - 3 = - 5 \cdot (x + 6)$

Step 5

Solve for $y$ .

Simplify $- 5 \cdot (x + 6)$ .

Rewrite.

$y - 3 = 0 + 0 - 5 \cdot (x + 6)$

Simplify by adding zeros.

$y - 3 = - 5 \cdot (x + 6)$

Apply the distributive property.

$y - 3 = - 5 x - 5 \cdot 6$

Multiply $- 5$ by $6$ .

$y - 3 = - 5 x - 30$

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

Add $3$ to both sides of the equation.

$y = - 5 x - 30 + 3$

Add $- 30$ and $3$ .

$y = - 5 x - 27$

Step 6

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

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