Pre-Algebra Examples

$(12, - 18)$ , $(- 15, - 19)$

Step 1

Find the value of the slope.

Tap for more steps...

Step 1.1

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 1.2

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 1.3

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

$m = \frac{- 19 - (- 18)}{- 15 - (12)}$

Step 1.4

Simplify.

Tap for more steps...

Step 1.4.1

Simplify the numerator.

Tap for more steps...

Step 1.4.1.1

Multiply $- 1$ by $- 18$ .

$m = \frac{- 19 + 18}{- 15 - (12)}$

Step 1.4.1.2

Add $- 19$ and $18$ .

$m = \frac{- 1}{- 15 - (12)}$

Step 1.4.2

Simplify the denominator.

Tap for more steps...

Step 1.4.2.1

Multiply $- 1$ by $12$ .

$m = \frac{- 1}{- 15 - 12}$

Step 1.4.2.2

Subtract $12$ from $- 15$ .

$m = \frac{- 1}{- 27}$

Step 1.4.3

Dividing two negative values results in a positive value.

$m = \frac{1}{27}$

Step 2

Find the value of the y-intercept.

Tap for more steps...

Step 2.1

Substitute the value of $m$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (\frac{1}{27}) x + b$

Step 2.2

Substitute the value of $x$ into the slope-intercept form of the equation, $y = m x + b$ .

$y = (\frac{1}{27}) \cdot (12) + b$

Step 2.3

Substitute the value of $y$ into the slope-intercept form of the equation, $y = m x + b$ .

$- 18 = (\frac{1}{27}) \cdot (12) + b$

Step 2.4

Rewrite the equation as $(\frac{1}{27}) \cdot (12) + b = - 18$ .

$(\frac{1}{27}) \cdot (12) + b = - 18$

Step 2.5

Simplify each term.

Tap for more steps...

Step 2.5.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.5.1.1

Factor $3$ out of $27$ .

$\frac{1}{3 (9)} \cdot 12 + b = - 18$

Step 2.5.1.2

Factor $3$ out of $12$ .

$\frac{1}{3 \cdot 9} \cdot (3 \cdot 4) + b = - 18$

Step 2.5.1.3

Cancel the common factor.

$\frac{1}{3 \cdot 9} \cdot (3 \cdot 4) + b = - 18$

Step 2.5.1.4

Rewrite the expression.

$\frac{1}{9} \cdot 4 + b = - 18$

Step 2.5.2

Combine $\frac{1}{9}$ and $4$ .

$\frac{4}{9} + b = - 18$

Step 2.6

Move all terms not containing $b$ to the right side of the equation.

Tap for more steps...

Step 2.6.1

Subtract $\frac{4}{9}$ from both sides of the equation.

$b = - 18 - \frac{4}{9}$

Step 2.6.2

To write $- 18$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$b = - 18 \cdot \frac{9}{9} - \frac{4}{9}$

Step 2.6.3

Combine $- 18$ and $\frac{9}{9}$ .

$b = \frac{- 18 \cdot 9}{9} - \frac{4}{9}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{- 18 \cdot 9 - 4}{9}$

Step 2.6.5

Simplify the numerator.

Tap for more steps...

Step 2.6.5.1

Multiply $- 18$ by $9$ .

$b = \frac{- 162 - 4}{9}$

Step 2.6.5.2

Subtract $4$ from $- 162$ .

$b = \frac{- 166}{9}$

Step 2.6.6

Move the negative in front of the fraction.

$b = - \frac{166}{9}$

Step 3

List the slope and y-intercept.

Slope: $\frac{1}{27}$

y-intercept: $(0, - \frac{166}{9})$

Step 4