Pre-Algebra Examples

$(- 3, 0)$ , $(0, - 3)$

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.

$m = \frac{- 3 - (0)}{0 - (- 3)}$

Step 1.4

Simplify.

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Step 1.4.1

Reduce the expression by cancelling the common factors.

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Step 1.4.1.1

Cancel the common factor of $- 3 - (0)$ and $0 - (- 3)$ .

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Step 1.4.1.1.1

Rewrite $- 3$ as $- 1 (3)$ .

$m = \frac{- 1 \cdot 3 - (0)}{0 - (- 3)}$

Step 1.4.1.1.2

Factor $- 1$ out of $- 1 (3) - (0)$ .

$m = \frac{- 1 (3 + 0)}{0 - (- 3)}$

Step 1.4.1.1.3

Reorder terms.

$m = \frac{- 1 (3 + 0)}{0 - 3 \cdot - 1}$

Step 1.4.1.1.4

Factor $3$ out of $- 1 (3 + 0)$ .

$m = \frac{3 (- 1 (1 + 0))}{0 - 3 \cdot - 1}$

Step 1.4.1.1.5

Cancel the common factors.

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Step 1.4.1.1.5.1

Factor $3$ out of $0$ .

$m = \frac{3 (- 1 (1 + 0))}{3 (0) - 3 \cdot - 1}$

Step 1.4.1.1.5.2

Factor $3$ out of $- 3 \cdot - 1$ .

$m = \frac{3 (- 1 (1 + 0))}{3 (0) + 3 (1)}$

Step 1.4.1.1.5.3

Factor $3$ out of $3 (0) + 3 (- - 1)$ .

$m = \frac{3 (- 1 (1 + 0))}{3 (0 + 1)}$

Step 1.4.1.1.5.4

Cancel the common factor.

$m = \frac{3 (- 1 (1 + 0))}{3 (0 + 1)}$

Step 1.4.1.1.5.5

Rewrite the expression.

$m = \frac{- 1 (1 + 0)}{0 + 1}$

Step 1.4.1.2

Add $1$ and $0$ .

$m = \frac{- 1 \cdot 1}{0 + 1}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{- 1 \cdot 1}{0 + 1}$

Step 1.4.2.2

Add $0$ and $1$ .

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

Step 1.4.3

Simplify the expression.

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Step 1.4.3.1

Multiply $- 1$ by $1$ .

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

Step 1.4.3.2

Divide $- 1$ by $1$ .

$m = - 1$

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, $y = m x + b$ .

$y = (- 1) \cdot x + b$

Step 2.2

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

$y = (- 1) \cdot (- 3) + b$

Step 2.3

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

$0 = (- 1) \cdot (- 3) + b$

Step 2.4

Rewrite the equation as $(- 1) \cdot (- 3) + b = 0$ .

$(- 1) \cdot (- 3) + b = 0$

Step 2.5

Multiply $- 1$ by $- 3$ .

$3 + b = 0$

Step 2.6

Subtract $3$ from both sides of the equation.

$b = - 3$

Step 3

List the slope and y-intercept.

Slope: $- 1$

y-intercept: $(0, - 3)$

Step 4