Algebra Examples

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

Find the value of the slope.

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Slope is equal to the change in $y$ over the change in $x$ , or rise over run.

$m = \frac{change in y}{change in x}$

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).

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

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

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

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $1$ to get $- 1$ .

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

Subtract $1$ from $0$ to get $- 1$ .

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

Simplify the denominator.

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Remove parentheses.

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

Multiply $- 1$ by $0$ to get $0$ .

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

Add $1$ and $0$ to get $1$ .

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

Divide $- 1$ by $1$ to get $- 1$ .

$m = - 1$

Find the value of the y-intercept.

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

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

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

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

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

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

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

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

Simplify the left side.

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Simplify each term.

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Multiply $- 1$ by $0$ to get $(- 1) (0)$ .

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

Multiply $- 1$ by $0$ to get $0$ .

$0 + b = 1$

Add $0$ and $b$ to get $b$ .

$b = 1$

The values of the slope and y-intercept are $m = - 1$ and $b = 1$

$m = - 1$

$b = 1$

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