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

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

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.

$y = m x + b$

Subtract $x$ from both sides of the equation.

$y = 3 - x$

Reorder $3$ and $- x$ .

$y = - x + 3$

Using the slope-intercept form, the slope is $- 1$ .

$m = - 1$

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

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

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

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

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

Solve for $y$ .

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

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Simplify the expression.

Rewrite $- 1 x$ as $- x$ .

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

Multiply $- 1$ by $3$ .

$y - 2 = - x - 3$

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

Add $2$ to both sides of the equation.

$y = - x - 3 + 2$

Add $- 3$ and $2$ .

$y = - x - 1$

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

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