Precalculus Examples

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

Choose a point that the parallel line will pass through.

$(0, 0)$

Rewrite in slope-intercept form.

Tap for more steps...

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 each term.

Tap for more steps...

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

Tap for more steps...

Write $x$ as a fraction with denominator $1$ .

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

Multiply $\frac{x}{1}$ and $\frac{3}{2}$ .

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

Move $3$ to the left of the expression $x \cdot 3$ .

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

Multiply $3$ by $x$ .

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

Rewrite in slope-intercept form.

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

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

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

To find an equation that is parallel to $y = - \frac{3}{2} x + 3$ , the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.

$(0, 0)$

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

Find the value of $b$ using the formula for the equation of a line.

Tap for more steps...

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Substitute the value of $m$ into the equation.

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

Substitute the value of $x$ into the equation.

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

Substitute the value of $y$ into the equation.

$(0) = (- \frac{3}{2}) \cdot (0) + b$

Find the value of $b$ .

Tap for more steps...

Rewrite the equation as $(- \frac{3}{2}) \cdot (0) + b = 0$ .

$(- \frac{3}{2}) \cdot (0) + b = 0$

Simplify the left side.

Tap for more steps...

Simplify each term.

Tap for more steps...

Multiply $- \frac{3}{2}$ by $0$ .

$(- \frac{3}{2}) (0) + b = 0$

Simplify $(- \frac{3}{2}) (0)$ .

Tap for more steps...

Multiply $0$ by $- 1$ .

$0 (\frac{3}{2}) + b = 0$

Multiply $0$ by $\frac{3}{2}$ .

$0 + b = 0$

Add $0$ and $b$ .

$b = 0$

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

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

Enter YOUR Problem