Algebra Examples

Passing through $(- 12, 0)$ and $(0, 12)$

Step 1

Find the slope of the line between $(- 12, 0)$ and $(0, 12)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

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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.

$m = \frac{12 - (0)}{0 - (- 12)}$

Step 1.4

Simplify.

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Step 1.4.1

Reduce the expression by cancelling the common factors.

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Step 1.4.1.1

Cancel the common factor of $12 - (0)$ and $0 - (- 12)$ .

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Step 1.4.1.1.1

Rewrite $12$ as $- 1 (- 12)$ .

$m = \frac{- 1 \cdot - 12 - (0)}{0 - (- 12)}$

Step 1.4.1.1.2

Factor $- 1$ out of $- 1 (- 12) - (0)$ .

$m = \frac{- 1 (- 12 + 0)}{0 - (- 12)}$

Step 1.4.1.1.3

Reorder terms.

$m = \frac{- 1 (- 12 + 0)}{0 - 12 \cdot - 1}$

Step 1.4.1.1.4

Factor $12$ out of $- 1 (- 12 + 0)$ .

$m = \frac{12 (- 1 (- 1 + 0))}{0 - 12 \cdot - 1}$

Step 1.4.1.1.5

Cancel the common factors.

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Step 1.4.1.1.5.1

Factor $12$ out of $0$ .

$m = \frac{12 (- 1 (- 1 + 0))}{12 (0) - 12 \cdot - 1}$

Step 1.4.1.1.5.2

Factor $12$ out of $- 12 \cdot - 1$ .

$m = \frac{12 (- 1 (- 1 + 0))}{12 (0) + 12 (1)}$

Step 1.4.1.1.5.3

Factor $12$ out of $12 (0) + 12 (- - 1)$ .

$m = \frac{12 (- 1 (- 1 + 0))}{12 (0 + 1)}$

Step 1.4.1.1.5.4

Cancel the common factor.

$m = \frac{12 (- 1 (- 1 + 0))}{12 (0 + 1)}$

Step 1.4.1.1.5.5

Rewrite the expression.

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

Step 1.4.1.2

Add $- 1$ and $0$ .

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

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $- 1$ .

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

Step 1.4.2.2

Add $0$ and $1$ .

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

Step 1.4.3

Simplify the expression.

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Step 1.4.3.1

Multiply $- 1$ by $- 1$ .

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

Step 1.4.3.2

Divide $1$ by $1$ .

$m = 1$

Step 2

Use the slope $1$ and a given point $(- 12, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = 1 \cdot (x - (- 12))$

Step 3

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

$y + 0 = 1 \cdot (x + 12)$

Step 4

Solve for $y$ .

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Step 4.1

Add $y$ and $0$ .

$y = 1 \cdot (x + 12)$

Step 4.2

Multiply $x + 12$ by $1$ .

$y = x + 12$

Step 5

List the equation in different forms.

Slope-intercept form:

$y = x + 12$

Point-slope form:

$y + 0 = 1 \cdot (x + 12)$

Step 6