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

$(1, 3)$ ; $y = 3 x + 2$

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

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

Step 4

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

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

Step 5

Solve for $y$ .

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

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

$y - 3 = 3 x - 3$

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

Add $3$ to both sides of the equation.

$y = 3 x - 3 + 3$

Combine the opposite terms in $3 x - 3 + 3$ .

Add $- 3$ and $3$ .

$y = 3 x + 0$

Add $3 x$ and $0$ .

$y = 3 x$

Step 6

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

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