Find Any Equation Parallel to the Line y-3=5(x-9)

$y - 3 = 5 (x - 9)$

Step 1

Choose a point that the parallel line will pass through.

$(0, 0)$

Step 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.

$y = m x + b$

Simplify the right side.

Simplify $5 (x - 9)$ .

Apply the distributive property.

$y - 3 = 5 x + 5 \cdot - 9$

Multiply $5$ by $- 9$ .

$y - 3 = 5 x - 45$

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

Add $3$ to both sides of the equation.

$y = 5 x - 45 + 3$

Add $- 45$ and $3$ .

$y = 5 x - 42$

Step 3

Using the slope-intercept form, the slope is $5$ .

$m = 5$

Step 4

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

Step 5

Use the slope $5$ and a given point $(0, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = 5 \cdot (x - (0))$

Step 6

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

$y + 0 = 5 \cdot (x + 0)$

Step 7

Solve for $y$ .

Add $y$ and $0$ .

$y = 5 \cdot (x + 0)$

Add $x$ and $0$ .

$y = 5 x$

Step 8

Find Any Equation Parallel to the Line y-3=5(x-9)

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