Find the Parallel Line Find the equation of the line through (7,2) which is parallel to the line y=-3x-2

Find the equation of the line through $(7, 2)$ which is parallel to the line $y = - 3 x - 2$

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 $- 3$ .

$m = - 3$

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 $- 3$ and a given point $(7, 2)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (2) = - 3 \cdot (x - (7))$

Step 4

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

$y - 2 = - 3 \cdot (x - 7)$

Step 5

Solve for $y$ .

Simplify $- 3 \cdot (x - 7)$ .

Rewrite.

$y - 2 = 0 + 0 - 3 \cdot (x - 7)$

Simplify by adding zeros.

$y - 2 = - 3 \cdot (x - 7)$

Apply the distributive property.

$y - 2 = - 3 x - 3 \cdot - 7$

Multiply $- 3$ by $- 7$ .

$y - 2 = - 3 x + 21$

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

Add $2$ to both sides of the equation.

$y = - 3 x + 21 + 2$

Add $21$ and $2$ .

$y = - 3 x + 23$

Step 6

Find the Parallel Line Find the equation of the line through (7,2) which is parallel to the line y=-3x-2

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