Precalculus Examples

$(- 6, 0)$ , $(0, - 3)$

Step 1

Find the slope of the line between $(- 6, 0)$ and $(0, - 3)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

Tap for more steps...

Step 1.1

Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

Step 1.2

The change in $x$ is equal to the difference in x-coordinates (also called run), and the change in $y$ is equal to the difference in y-coordinates (also called rise).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 1.3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 3 - (0)}{0 - (- 6)}$

Step 1.4

Simplify.

Tap for more steps...

Step 1.4.1

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 1.4.1.1

Cancel the common factor of $- 3 - (0)$ and $0 - (- 6)$ .

Tap for more steps...

Step 1.4.1.1.1

Rewrite $- 3$ as $- 1 (3)$ .

$m = \frac{- 1 \cdot 3 - (0)}{0 - (- 6)}$

Step 1.4.1.1.2

Factor $- 1$ out of $- 1 (3) - (0)$ .

$m = \frac{- 1 (3 + 0)}{0 - (- 6)}$

Step 1.4.1.1.3

Reorder terms.

$m = \frac{- 1 (3 + 0)}{0 - 6 \cdot - 1}$

Step 1.4.1.1.4

Factor $3$ out of $- 1 (3 + 0)$ .

$m = \frac{3 (- 1 (1 + 0))}{0 - 6 \cdot - 1}$

Step 1.4.1.1.5

Cancel the common factors.

Tap for more steps...

Step 1.4.1.1.5.1

Factor $3$ out of $0$ .

$m = \frac{3 (- 1 (1 + 0))}{3 (0) - 6 \cdot - 1}$

Step 1.4.1.1.5.2

Factor $3$ out of $- 6 \cdot - 1$ .

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

Step 1.4.1.1.5.3

Factor $3$ out of $3 (0) + 3 (- 2 \cdot - 1)$ .

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

Step 1.4.1.1.5.4

Cancel the common factor.

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

Step 1.4.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (1 + 0)}{0 - 2 \cdot - 1}$

Step 1.4.1.2

Add $1$ and $0$ .

$m = \frac{- 1 \cdot 1}{0 - 2 \cdot - 1}$

Step 1.4.2

Simplify the denominator.

Tap for more steps...

Step 1.4.2.1

Multiply $- 2$ by $- 1$ .

$m = \frac{- 1 \cdot 1}{0 + 2}$

Step 1.4.2.2

Add $0$ and $2$ .

$m = \frac{- 1 \cdot 1}{2}$

Step 1.4.3

Simplify the expression.

Tap for more steps...

Step 1.4.3.1

Multiply $- 1$ by $1$ .

$m = \frac{- 1}{2}$

Step 1.4.3.2

Move the negative in front of the fraction.

$m = - \frac{1}{2}$

Step 2

Use the slope $- \frac{1}{2}$ and a given point $(- 6, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{1}{2} \cdot (x - (- 6))$

Step 3

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

$y + 0 = - \frac{1}{2} \cdot (x + 6)$

Step 4

Solve for $y$ .

Tap for more steps...

Step 4.1

Add $y$ and $0$ .

$y = - \frac{1}{2} \cdot (x + 6)$

Step 4.2

Simplify $- \frac{1}{2} \cdot (x + 6)$ .

Tap for more steps...

Step 4.2.1

Apply the distributive property.

$y = - \frac{1}{2} x - \frac{1}{2} \cdot 6$

Step 4.2.2

Combine $x$ and $\frac{1}{2}$ .

$y = - \frac{x}{2} - \frac{1}{2} \cdot 6$

Step 4.2.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$y = - \frac{x}{2} + \frac{- 1}{2} \cdot 6$

Step 4.2.3.2

Factor $2$ out of $6$ .

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

Step 4.2.3.3

Cancel the common factor.

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

Step 4.2.3.4

Rewrite the expression.

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

Step 4.2.4

Multiply $- 1$ by $3$ .

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

Step 5

Reorder terms.

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

Step 6

Remove parentheses.

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

Step 7

List the equation in different forms.

Slope-intercept form:

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

Point-slope form:

$y + 0 = - \frac{1}{2} \cdot (x + 6)$

Step 8