Pre-Algebra Examples

$(2, - 5)$ , $(7, - 1)$

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.

$m = \frac{- 1 - (- 5)}{7 - (2)}$

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 $- 5$ .

$m = \frac{- 1 + 5}{7 - (2)}$

Step 5.1.2

Add $- 1$ and $5$ .

$m = \frac{4}{7 - (2)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply $- 1$ by $2$ .

$m = \frac{4}{7 - 2}$

Step 5.2.2

Subtract $2$ from $7$ .

$m = \frac{4}{5}$

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.

$y = (\frac{4}{5}) x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (\frac{4}{5}) \cdot (2) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$- 5 = (\frac{4}{5}) \cdot (2) + b$

Step 6.5

Find the value of $b$ .

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Step 6.5.1

Rewrite the equation as $\frac{4}{5} \cdot 2 + b = - 5$ .

$\frac{4}{5} \cdot 2 + b = - 5$

Step 6.5.2

Multiply $\frac{4}{5} \cdot 2$ .

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Step 6.5.2.1

Combine $\frac{4}{5}$ and $2$ .

$\frac{4 \cdot 2}{5} + b = - 5$

Step 6.5.2.2

Multiply $4$ by $2$ .

$\frac{8}{5} + b = - 5$

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 $\frac{8}{5}$ from both sides of the equation.

$b = - 5 - \frac{8}{5}$

Step 6.5.3.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = - 5 \cdot \frac{5}{5} - \frac{8}{5}$

Step 6.5.3.3

Combine $- 5$ and $\frac{5}{5}$ .

$b = \frac{- 5 \cdot 5}{5} - \frac{8}{5}$

Step 6.5.3.4

Combine the numerators over the common denominator.

$b = \frac{- 5 \cdot 5 - 8}{5}$

Step 6.5.3.5

Simplify the numerator.

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Step 6.5.3.5.1

Multiply $- 5$ by $5$ .

$b = \frac{- 25 - 8}{5}$

Step 6.5.3.5.2

Subtract $8$ from $- 25$ .

$b = \frac{- 33}{5}$

Step 6.5.3.6

Move the negative in front of the fraction.

$b = - \frac{33}{5}$

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.

$y = \frac{4}{5} x - \frac{33}{5}$

Step 8