Precalculus Examples

$(- a + 3, b - 3)$ and $(a + 3, - b)$

Step 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 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 3

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

$m = \frac{- b - (b - 3)}{a + 3 - (- a + 3)}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Apply the distributive property.

$m = \frac{- b - b + 3}{a + 3 - (- a + 3)}$

Step 4.1.2

Multiply $- 1$ by $- 3$ .

$m = \frac{- b - b + 3}{a + 3 - (- a + 3)}$

Step 4.1.3

Subtract $b$ from $- b$ .

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

Step 4.2

Simplify the denominator.

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Step 4.2.1

Apply the distributive property.

$m = \frac{- 2 b + 3}{a + 3 + a - 1 \cdot 3}$

Step 4.2.2

Multiply $- - a$ .

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Step 4.2.2.1

Multiply $- 1$ by $- 1$ .

$m = \frac{- 2 b + 3}{a + 3 + 1 a - 1 \cdot 3}$

Step 4.2.2.2

Multiply $a$ by $1$ .

$m = \frac{- 2 b + 3}{a + 3 + a - 1 \cdot 3}$

Step 4.2.3

Multiply $- 1$ by $3$ .

$m = \frac{- 2 b + 3}{a + 3 + a - 3}$

Step 4.2.4

Add $a$ and $a$ .

$m = \frac{- 2 b + 3}{2 a + 3 - 3}$

Step 4.2.5

Subtract $3$ from $3$ .

$m = \frac{- 2 b + 3}{2 a + 0}$

Step 4.2.6

Add $2 a$ and $0$ .

$m = \frac{- 2 b + 3}{2 a}$

Step 4.3

Simplify with factoring out.

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Step 4.3.1

Factor $- 1$ out of $- 2 b$ .

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

Step 4.3.2

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

$m = \frac{- (2 b) - 1 \cdot - 3}{2 a}$

Step 4.3.3

Factor $- 1$ out of $- (2 b) - 1 (- 3)$ .

$m = \frac{- (2 b - 3)}{2 a}$

Step 4.3.4

Simplify the expression.

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Step 4.3.4.1

Rewrite $- (2 b - 3)$ as $- 1 (2 b - 3)$ .

$m = \frac{- 1 (2 b - 3)}{2 a}$

Step 4.3.4.2

Move the negative in front of the fraction.

$m = - \frac{2 b - 3}{2 a}$