Find the Parallel Line -3x+y=15 (1,2)

$- 3 x + y = 15$ $(1, 2)$

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.

$y = m x + b$

Add $3 x$ to both sides of the equation.

$y = 15 + 3 x$

Reorder $15$ and $3 x$ .

$y = 3 x + 15$

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

$m = 3$

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

Use the slope $3$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

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

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

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.

Add $2$ to both sides of the equation.

$y = 3 x - 3 + 2$

Add $- 3$ and $2$ .

$y = 3 x - 1$

Find the Parallel Line -3x+y=15 (1,2)

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