Algebra Examples

$(1, - 2)$ , $(3, 6)$

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.

$m = \frac{6 - (- 2)}{3 - (1)}$

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $- 2$ to get $2$ .

$m = \frac{6 + 2}{3 - (1)}$

Add $6$ and $2$ to get $8$ .

$m = \frac{8}{3 - (1)}$

Simplify the denominator.

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Remove parentheses.

$m = \frac{8}{3 - (1)}$

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

$m = \frac{8}{3 - 1}$

Subtract $1$ from $3$ to get $2$ .

$m = \frac{8}{2}$

Divide $8$ by $2$ to get $4$ .

$m = 4$

Find the value of the y-intercept.

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

$y = (4) \cdot x + b$

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

$y = (4) \cdot (1) + b$

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

$(- 2) = (4) \cdot (1) + b$

Rewrite the equation as $(4) \cdot (1) + b = - 2$ .

$(4) \cdot (1) + b = - 2$

Simplify each term.

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Multiply $4$ by $1$ to get $(4) (1)$ .

$(4) (1) + b = - 2$

Multiply $4$ by $1$ to get $4$ .

$4 + b = - 2$

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

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Since $4$ does not contain the variable to solve for, move it to the right side of the equation by subtracting $4$ from both sides.

$b = - 4 - 2$

Subtract $2$ from $- 4$ to get $- 6$ .

$b = - 6$

The values of the slope and y-intercept are $m = 4$ and $b = - 6$

$m = 4$

$b = - 6$

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