Find Any Equation Parallel to the Line y=1/3x+3

$y = \frac{1}{3} x + 3$

Choose a point that the parallel line will pass through.

$(0, 0)$

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.

Combine $\frac{1}{3}$ and $x$ .

$y = \frac{x}{3} + 3$

Reorder terms.

$y = \frac{1}{3} x + 3$

Using the slope-intercept form, the slope is $\frac{1}{3}$ .

$m = \frac{1}{3}$

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

Use the slope $\frac{1}{3}$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = \frac{1}{3} \cdot (x - (0))$

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

$y + 0 = \frac{1}{3} \cdot (x + 0)$

Solve for $y$ .

Add $y$ and $0$ .

$y = \frac{1}{3} \cdot (x + 0)$

Simplify $\frac{1}{3} \cdot (x + 0)$ .

Add $x$ and $0$ .

$y = \frac{1}{3} \cdot x$

Combine $\frac{1}{3}$ and $x$ .

$y = \frac{x}{3}$

Reorder terms.

$y = \frac{1}{3} x$

Find Any Equation Parallel to the Line y=1/3x+3

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