Algebra Examples

$(- 1, 0)$ and $(4, - 5)$

Step 1

Find the slope of the line between $(- 1, 0)$ and $(4, - 5)$ 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.

$m = \frac{- 5 - (0)}{4 - (- 1)}$

Step 1.4

Simplify.

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Step 1.4.1

Simplify the numerator.

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Step 1.4.1.1

Multiply $- 1$ by $0$ .

$m = \frac{- 5 + 0}{4 - (- 1)}$

Step 1.4.1.2

Add $- 5$ and $0$ .

$m = \frac{- 5}{4 - (- 1)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{- 5}{4 + 1}$

Step 1.4.2.2

Add $4$ and $1$ .

$m = \frac{- 5}{5}$

Step 1.4.3

Divide $- 5$ by $5$ .

$m = - 1$

Step 2

Use the slope $- 1$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

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

Step 3

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

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

Step 4

Solve for $y$ .

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Step 4.1

Add $y$ and $0$ .

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

Step 4.2

Simplify $- 1 \cdot (x + 1)$ .

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Step 4.2.1

Apply the distributive property.

$y = - 1 x - 1 \cdot 1$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Rewrite $- 1 x$ as $- x$ .

$y = - x - 1 \cdot 1$

Step 4.2.2.2

Multiply $- 1$ by $1$ .

$y = - x - 1$

Step 5