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

through: $(- 1, 4)$ ; parallel to $y = - 5 x + 2$

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

$y - (4) = - 5 \cdot (x - (- 1))$

Step 4

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

$y - 4 = - 5 \cdot (x + 1)$

Step 5

Solve for $y$ .

Simplify $- 5 \cdot (x + 1)$ .

Rewrite.

$y - 4 = 0 + 0 - 5 \cdot (x + 1)$

Simplify by adding zeros.

$y - 4 = - 5 \cdot (x + 1)$

Apply the distributive property.

$y - 4 = - 5 x - 5 \cdot 1$

Multiply $- 5$ by $1$ .

$y - 4 = - 5 x - 5$

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

Add $4$ to both sides of the equation.

$y = - 5 x - 5 + 4$

Add $- 5$ and $4$ .

$y = - 5 x - 1$

Step 6

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

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