Algebra Examples

(0, 9)

$(0, 9)$ ,

(8, 6)

$(8, 6)$

Step 1

Find the slope of the line between

(0, 9)

$(0, 9)$ and

(8, 6)

$(8, 6)$ 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 - (9)}{8 - (0)}

$m = \frac{6 - (9)}{8 - (0)}$

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

9

$9$ .

m = \frac{6 - 9}{8 - (0)}

$m = \frac{6 - 9}{8 - (0)}$

Step 1.4.1.2

Subtract

9

$9$ from

6

$6$ .

m = \frac{- 3}{8 - (0)}

$m = \frac{- 3}{8 - (0)}$

m = \frac{- 3}{8 - (0)}

$m = \frac{- 3}{8 - (0)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply

- 1

$- 1$ by

0

$0$ .

m = \frac{- 3}{8 + 0}

$m = \frac{- 3}{8 + 0}$

Step 1.4.2.2

Add

8

$8$ and

0

$0$ .

m = \frac{- 3}{8}

$m = \frac{- 3}{8}$

m = \frac{- 3}{8}

$m = \frac{- 3}{8}$

Step 1.4.3

Move the negative in front of the fraction.

m = - \frac{3}{8}

$m = - \frac{3}{8}$

m = - \frac{3}{8}

$m = - \frac{3}{8}$

m = - \frac{3}{8}

$m = - \frac{3}{8}$

Step 2

Use the slope

- \frac{3}{8}

$- \frac{3}{8}$ and a given point

(0, 9)

$(0, 9)$ 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 - (9) = - \frac{3}{8} \cdot (x - (0))

$y - (9) = - \frac{3}{8} \cdot (x - (0))$

Step 3

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

y - 9 = - \frac{3}{8} \cdot (x + 0)

$y - 9 = - \frac{3}{8} \cdot (x + 0)$

Step 4

Solve for

y

$y$ .

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Step 4.1

Simplify

- \frac{3}{8} \cdot (x + 0)

$- \frac{3}{8} \cdot (x + 0)$ .

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Step 4.1.1

Add

x

$x$ and

0

$0$ .

y - 9 = - \frac{3}{8} \cdot x

$y - 9 = - \frac{3}{8} \cdot x$

Step 4.1.2

Combine

x

$x$ and

\frac{3}{8}

$\frac{3}{8}$ .

y - 9 = - \frac{x \cdot 3}{8}

$y - 9 = - \frac{x \cdot 3}{8}$

Step 4.1.3

Move

3

$3$ to the left of

x

$x$ .

y - 9 = - \frac{3 x}{8}

$y - 9 = - \frac{3 x}{8}$

y - 9 = - \frac{3 x}{8}

$y - 9 = - \frac{3 x}{8}$

Step 4.2

Add

9

$9$ to both sides of the equation.

y = - \frac{3 x}{8} + 9

$y = - \frac{3 x}{8} + 9$

y = - \frac{3 x}{8} + 9

$y = - \frac{3 x}{8} + 9$

Step 5

Reorder terms.

y = - (\frac{3}{8} x) + 9

$y = - (\frac{3}{8} x) + 9$

Step 6

Remove parentheses.

y = - \frac{3}{8} x + 9

$y = - \frac{3}{8} x + 9$

Step 7

List the equation in different forms.

Slope-intercept form:

y = - \frac{3}{8} x + 9

$y = - \frac{3}{8} x + 9$

Point-slope form:

y - 9 = - \frac{3}{8} \cdot (x + 0)

$y - 9 = - \frac{3}{8} \cdot (x + 0)$

Step 8

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