Precalculus Examples

$(0, 1)$ , $(1, 0)$

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.

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

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 $1$ .

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

Step 1.4.1.2

Subtract $1$ from $0$ .

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

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $0$ .

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

Step 1.4.2.2

Add $1$ and $0$ .

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

Step 1.4.3

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, $y = m x + b$ .

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

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

Simplify $(- 1) \cdot (0) + b$ .

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Step 2.5.1

Multiply $- 1$ by $0$ .

$0 + b = 1$

Step 2.5.2

Add $0$ and $b$ .

$b = 1$

Step 3

List the slope and y-intercept.

Slope: $- 1$

y-intercept: $(0, 1)$

Step 4

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