Algebra Examples

(0, 0)

$(0, 0)$ ,

(- 6, 6)

$(- 6, 6)$

Step 1

Find the slope of the line between

(0, 0)

$(0, 0)$ and

(- 6, 6)

$(- 6, 6)$ using

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

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of

y

$y$ over the change of

x

$x$ .

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Step 1.1

Slope is equal to the change in

y

$y$ over the change in

x

$x$ , or rise over run.

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

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

Step 1.2

The change in

x

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

y

$y$ is equal to the difference in y-coordinates (also called rise).

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

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

Step 1.3

Substitute in the values of

x

$x$ and

y

$y$ into the equation to find the slope.

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

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

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

$- 1$ by

0

$0$ .

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

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

Step 1.4.1.2

Add

6

$6$ and

0

$0$ .

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

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

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

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

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply

- 1

$- 1$ by

0

$0$ .

m = \frac{6}{- 6 + 0}

$m = \frac{6}{- 6 + 0}$

Step 1.4.2.2

Add

- 6

$- 6$ and

0

$0$ .

m = \frac{6}{- 6}

$m = \frac{6}{- 6}$

m = \frac{6}{- 6}

$m = \frac{6}{- 6}$

Step 1.4.3

Divide

6

$6$ by

- 6

$- 6$ .

m = - 1

$m = - 1$

m = - 1

$m = - 1$

m = - 1

$m = - 1$

Step 2

Use the slope

- 1

$- 1$ and a given point

(0, 0)

$(0, 0)$ to substitute for

x_{1}

$x_{1}$ and

y_{1}

$y_{1}$ in the point-slope form

y - y_{1} = m (x - x_{1})

$y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation

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

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

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

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

Step 3

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

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

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

Step 4

Solve for

y

$y$ .

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Step 4.1

Add

y

$y$ and

0

$0$ .

y = - 1 \cdot (x + 0)

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

Step 4.2

Simplify

- 1 \cdot (x + 0)

$- 1 \cdot (x + 0)$ .

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Step 4.2.1

Add

x

$x$ and

0

$0$ .

y = - 1 \cdot x

$y = - 1 \cdot x$

Step 4.2.2

Rewrite

- 1 x

$- 1 x$ as

- x

$- x$ .

y = - x

$y = - x$

y = - x

$y = - x$

y = - x

$y = - x$

Step 5

List the equation in different forms.

Slope-intercept form:

y = - x

$y = - x$

Point-slope form:

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

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

Step 6

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