Algebra Examples

$(2, - 3)$ , $(- 4, - 12)$

Step 1

Find the value of the slope.

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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.

$m = \frac{- 12 - (- 3)}{- 4 - (2)}$

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 $- 1$ by $- 3$ .

$m = \frac{- 12 + 3}{- 4 - (2)}$

Step 1.4.1.2

Add $- 12$ and $3$ .

$m = \frac{- 9}{- 4 - (2)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $2$ .

$m = \frac{- 9}{- 4 - 2}$

Step 1.4.2.2

Subtract $2$ from $- 4$ .

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

Step 1.4.3

Cancel the common factor of $- 9$ and $- 6$ .

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Step 1.4.3.1

Factor $- 3$ out of $- 9$ .

$m = \frac{- 3 \cdot 3}{- 6}$

Step 1.4.3.2

Cancel the common factors.

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Step 1.4.3.2.1

Factor $- 3$ out of $- 6$ .

$m = \frac{- 3 \cdot 3}{- 3 \cdot 2}$

Step 1.4.3.2.2

Cancel the common factor.

$m = \frac{- 3 \cdot 3}{- 3 \cdot 2}$

Step 1.4.3.2.3

Rewrite the expression.

$m = \frac{3}{2}$

Step 2

Find the value of the y-intercept.

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Step 2.1

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

$y = (\frac{3}{2}) x + b$

Step 2.2

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

$y = (\frac{3}{2}) \cdot (2) + b$

Step 2.3

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

$- 3 = (\frac{3}{2}) \cdot (2) + b$

Step 2.4

Rewrite the equation as $(\frac{3}{2}) \cdot (2) + b = - 3$ .

$(\frac{3}{2}) \cdot (2) + b = - 3$

Step 2.5

Cancel the common factor of $2$ .

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Step 2.5.1

Cancel the common factor.

$\frac{3}{2} \cdot 2 + b = - 3$

Step 2.5.2

Rewrite the expression.

$3 + b = - 3$

Step 2.6

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

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Step 2.6.1

Subtract $3$ from both sides of the equation.

$b = - 3 - 3$

Step 2.6.2

Subtract $3$ from $- 3$ .

$b = - 6$

Step 3

List the slope and y-intercept.

Slope: $\frac{3}{2}$

y-intercept: $(0, - 6)$

Step 4