Algebra Examples

(6, - 6)

$(6, - 6)$ ,

(8, 8)

$(8, 8)$

Step 1

Use

y = m x + b

$y = m x + b$ to calculate the equation of the line, where

m

$m$ represents the slope and

b

$b$ represents the y-intercept.

To calculate the equation of the line, use the

y = m x + b

$y = m x + b$ format.

Step 2

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 3

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 4

Substitute in the values of

x

$x$ and

y

$y$ into the equation to find the slope.

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

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

Step 5

Finding the slope

m

$m$ .

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Step 5.1

Cancel the common factor of

8 - (- 6)

$8 - (- 6)$ and

8 - (6)

$8 - (6)$ .

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Step 5.1.1

Rewrite

8

$8$ as

- 1 (- 8)

$- 1 (- 8)$ .

m = \frac{8 - (- 6)}{- 1 \cdot - 8 - (6)}

$m = \frac{8 - (- 6)}{- 1 \cdot - 8 - (6)}$

Step 5.1.2

Factor

- 1

$- 1$ out of

- 1 (- 8) - (6)

$- 1 (- 8) - (6)$ .

m = \frac{8 - (- 6)}{- 1 (- 8 + 6)}

$m = \frac{8 - (- 6)}{- 1 (- 8 + 6)}$

Step 5.1.3

Reorder terms.

m = \frac{8 - 6 \cdot - 1}{- 1 (- 8 + 6)}

$m = \frac{8 - 6 \cdot - 1}{- 1 (- 8 + 6)}$

Step 5.1.4

Factor

2

$2$ out of

8

$8$ .

m = \frac{2 (4) - 6 \cdot - 1}{- 1 (- 8 + 6)}

$m = \frac{2 (4) - 6 \cdot - 1}{- 1 (- 8 + 6)}$

Step 5.1.5

Factor

2

$2$ out of

- 6 \cdot - 1

$- 6 \cdot - 1$ .

m = \frac{2 (4) + 2 (- 3 \cdot - 1)}{- 1 (- 8 + 6)}

$m = \frac{2 (4) + 2 (- 3 \cdot - 1)}{- 1 (- 8 + 6)}$

Step 5.1.6

Factor

2

$2$ out of

2 (4) + 2 (- 3 \cdot - 1)

$2 (4) + 2 (- 3 \cdot - 1)$ .

m = \frac{2 (4 - 3 \cdot - 1)}{- 1 (- 8 + 6)}

$m = \frac{2 (4 - 3 \cdot - 1)}{- 1 (- 8 + 6)}$

Step 5.1.7

Cancel the common factors.

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Step 5.1.7.1

Factor

2

$2$ out of

- 1 (- 8 + 6)

$- 1 (- 8 + 6)$ .

m = \frac{2 (4 - 3 \cdot - 1)}{2 (- 1 (- 4 + 3))}

$m = \frac{2 (4 - 3 \cdot - 1)}{2 (- 1 (- 4 + 3))}$

Step 5.1.7.2

Cancel the common factor.

$m = \frac{2 (4 - 3 \cdot - 1)}{2 (- 1 (- 4 + 3))}$

Step 5.1.7.3

Rewrite the expression.

$m = \frac{4 - 3 \cdot - 1}{- 1 (- 4 + 3)}$

Step 5.2

Simplify the numerator.

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Step 5.2.1

Multiply

$- 3$ by

$- 1$ .

$m = \frac{4 + 3}{- 1 (- 4 + 3)}$

Step 5.2.2

Add

$4$ and

$3$ .

$m = \frac{7}{- 1 (- 4 + 3)}$

Step 5.3

Simplify the expression.

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Step 5.3.1

Add

$- 4$ and

$3$ .

$m = \frac{7}{- 1 \cdot - 1}$

Step 5.3.2

Multiply

$- 1$ by

$- 1$ .

$m = \frac{7}{1}$

Step 5.3.3

Divide

$7$ by

$1$ .

$m = 7$

Step 6

Find the value of

$b$ using the formula for the equation of a line.

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Step 6.1

Use the formula for the equation of a line to find

$b$ .

$y = m x + b$

Step 6.2

Substitute the value of

$m$ into the equation.

$y = (7) \cdot x + b$

Step 6.3

Substitute the value of

$x$ into the equation.

$y = (7) \cdot (6) + b$

Step 6.4

Substitute the value of

$y$ into the equation.

$- 6 = (7) \cdot (6) + b$

Step 6.5

Find the value of

$b$ .

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Step 6.5.1

Rewrite the equation as

$(7) \cdot (6) + b = - 6$ .

$(7) \cdot (6) + b = - 6$

Step 6.5.2

Multiply

$7$ by

$6$ .

$42 + b = - 6$

Step 6.5.3

Move all terms not containing

$b$ to the right side of the equation.

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Step 6.5.3.1

Subtract

$42$ from both sides of the equation.

$b = - 6 - 42$

Step 6.5.3.2

Subtract

$42$ from

$- 6$ .

$b = - 48$

Step 7

Now that the values of

$m$ (slope) and

$b$ (y-intercept) are known, substitute them into

$y = m x + b$ to find the equation of the line.

$y = 7 x - 48$

Step 8