Algebra Examples

$(- 9, 7)$ and $(- 6, - 3)$

Step 1

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

Step 2

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 3

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 4

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{- 3 - (7)}{- 6 - (- 9)}$

Step 5

Finding the slope $m$ .

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply $- 1$ by $7$ .

$m = \frac{- 3 - 7}{- 6 - (- 9)}$

Step 5.1.2

Subtract $7$ from $- 3$ .

$m = \frac{- 10}{- 6 - (- 9)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 1$ by $- 9$ .

$m = \frac{- 10}{- 6 + 9}$

Step 5.2.2

Add $- 6$ and $9$ .

$m = \frac{- 10}{3}$

Step 5.3

Move the negative in front of the fraction.

$m = - \frac{10}{3}$

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.

$y = (- \frac{10}{3}) \cdot x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (- \frac{10}{3}) \cdot (- 9) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$7 = (- \frac{10}{3}) \cdot (- 9) + b$

Step 6.5

Find the value of $b$ .

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Step 6.5.1

Rewrite the equation as $- \frac{10}{3} \cdot - 9 + b = 7$ .

$- \frac{10}{3} \cdot - 9 + b = 7$

Step 6.5.2

Simplify each term.

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Step 6.5.2.1

Cancel the common factor of $3$ .

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Step 6.5.2.1.1

Move the leading negative in $- \frac{10}{3}$ into the numerator.

$\frac{- 10}{3} \cdot - 9 + b = 7$

Step 6.5.2.1.2

Factor $3$ out of $- 9$ .

$\frac{- 10}{3} \cdot (3 (- 3)) + b = 7$

Step 6.5.2.1.3

Cancel the common factor.

$\frac{- 10}{3} \cdot (3 \cdot - 3) + b = 7$

Step 6.5.2.1.4

Rewrite the expression.

$- 10 \cdot - 3 + b = 7$

Step 6.5.2.2

Multiply $- 10$ by $- 3$ .

$30 + b = 7$

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 $30$ from both sides of the equation.

$b = 7 - 30$

Step 6.5.3.2

Subtract $30$ from $7$ .

$b = - 23$

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.

$y = - \frac{10}{3} x - 23$

Step 8