Algebra Examples

$(2, - 4)$ and $(0, - 4)$

Step 1

Find the slope of the line between $(2, - 4)$ and $(0, - 4)$ 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.

$m = \frac{- 4 - (- 4)}{0 - (2)}$

Step 1.4

Simplify.

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Step 1.4.1

Cancel the common factor of $- 4 - (- 4)$ and $0 - (2)$ .

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Step 1.4.1.1

Rewrite $0$ as $- 1 (0)$ .

$m = \frac{- 4 - (- 4)}{- 1 \cdot 0 - (2)}$

Step 1.4.1.2

Factor $- 1$ out of $- 1 (0) - (2)$ .

$m = \frac{- 4 - (- 4)}{- 1 (0 + 2)}$

Step 1.4.1.3

Reorder terms.

$m = \frac{- 4 - 4 \cdot - 1}{- 1 (0 + 2)}$

Step 1.4.1.4

Factor $2$ out of $- 4$ .

$m = \frac{2 (- 2) - 4 \cdot - 1}{- 1 (0 + 2)}$

Step 1.4.1.5

Factor $2$ out of $- 4 \cdot - 1$ .

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

Step 1.4.1.6

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

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

Step 1.4.1.7

Cancel the common factors.

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Step 1.4.1.7.1

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

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

Step 1.4.1.7.2

Cancel the common factor.

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

Step 1.4.1.7.3

Rewrite the expression.

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

Step 1.4.2

Simplify the numerator.

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Step 1.4.2.1

Multiply $- 2$ by $- 1$ .

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

Step 1.4.2.2

Add $- 2$ and $2$ .

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

Step 1.4.3

Simplify the expression.

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Step 1.4.3.1

Add $0$ and $1$ .

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

Step 1.4.3.2

Multiply $- 1$ by $1$ .

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

Step 1.4.3.3

Divide $0$ by $- 1$ .

$m = 0$

Step 2

Use the slope $0$ and a given point $(2, - 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 4) = 0 \cdot (x - (2))$

Step 3

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

$y + 4 = 0 \cdot (x - 2)$

Step 4

Solve for $y$ .

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Step 4.1

Multiply $0$ by $x - 2$ .

$y + 4 = 0$

Step 4.2

Subtract $4$ from both sides of the equation.

$y = - 4$

Step 5