Find Any Equation Parallel to the Line y=-3/2x-0

$y = - \frac{3}{2} x - 0$

Step 1

Choose a point that the parallel line will pass through.

$(1, 0)$

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 $- \frac{3}{2} x - 0$ .

Combine $x$ and $\frac{3}{2}$ .

$y = - \frac{x \cdot 3}{2} - 0$

Simplify the expression.

Move $3$ to the left of $x$ .

$y = - \frac{3 \cdot x}{2} - 0$

Subtract $0$ from $- \frac{3 x}{2}$ .

$y = - \frac{3 x}{2}$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{3}{2} x)$

Remove parentheses.

$y = - \frac{3}{2} x$

Step 3

Using the slope-intercept form, the slope is $- \frac{3}{2}$ .

$m = - \frac{3}{2}$

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 $- \frac{3}{2}$ and a given point $(1, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{3}{2} \cdot (x - (1))$

Step 6

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

$y + 0 = - \frac{3}{2} \cdot (x - 1)$

Step 7

Solve for $y$ .

Add $y$ and $0$ .

$y = - \frac{3}{2} \cdot (x - 1)$

Simplify $- \frac{3}{2} \cdot (x - 1)$ .

Apply the distributive property.

$y = - \frac{3}{2} x - \frac{3}{2} \cdot - 1$

Combine $x$ and $\frac{3}{2}$ .

$y = - \frac{x \cdot 3}{2} - \frac{3}{2} \cdot - 1$

Multiply $- \frac{3}{2} \cdot - 1$ .

Multiply $- 1$ by $- 1$ .

$y = - \frac{x \cdot 3}{2} + 1 (\frac{3}{2})$

Multiply $\frac{3}{2}$ by $1$ .

$y = - \frac{x \cdot 3}{2} + \frac{3}{2}$

Move $3$ to the left of $x$ .

$y = - \frac{3 x}{2} + \frac{3}{2}$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{3}{2} x) + \frac{3}{2}$

Remove parentheses.

$y = - \frac{3}{2} x + \frac{3}{2}$

Step 8

Find Any Equation Parallel to the Line y=-3/2x-0

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