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

$y = 3 x + 1$

Step 1

Choose a point that the parallel line will pass through.

$(0, 0)$

Step 2

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 3

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

Step 4

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

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

Step 5

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

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

Step 6

Solve for $y$ .

Add $y$ and $0$ .

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

Add $x$ and $0$ .

$y = 3 x$

Step 7

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

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