Find the Parallel Line y=5x+7 ; (3,18)

$y = 5 x + 7$ ; $(3, 18)$

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 $(3, 18)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (18) = 5 \cdot (x - (3))$

Step 4

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

$y - 18 = 5 \cdot (x - 3)$

Step 5

Solve for $y$ .

Simplify $5 \cdot (x - 3)$ .

Rewrite.

$y - 18 = 0 + 0 + 5 \cdot (x - 3)$

Simplify by adding zeros.

$y - 18 = 5 \cdot (x - 3)$

Apply the distributive property.

$y - 18 = 5 x + 5 \cdot - 3$

Multiply $5$ by $- 3$ .

$y - 18 = 5 x - 15$

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

Add $18$ to both sides of the equation.

$y = 5 x - 15 + 18$

Add $- 15$ and $18$ .

$y = 5 x + 3$

Step 6

Find the Parallel Line y=5x+7 ; (3,18)

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