Algebra Examples

$(6, 6)$ , $(3, 1)$

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.

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

Simplify.

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Simplify the numerator.

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Multiply $- 1$ by $6$ .

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

Subtract $6$ from $1$ .

$m = \frac{- 5}{3 - (6)}$

Simplify the denominator.

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Multiply $- 1$ by $6$ .

$m = \frac{- 5}{3 - 6}$

Subtract $6$ from $3$ .

$m = \frac{- 5}{- 3}$

Dividing two negative values results in a positive value.

$m = \frac{5}{3}$

Find the value of the y-intercept.

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

$y = (\frac{5}{3}) x + b$

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

$y = (\frac{5}{3}) \cdot (6) + b$

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

$6 = (\frac{5}{3}) \cdot (6) + b$

Rewrite the equation as $(\frac{5}{3}) \cdot (6) + b = 6$ .

$(\frac{5}{3}) \cdot (6) + b = 6$

Simplify each term.

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Cancel the common factor of $3$ .

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Factor $3$ out of $6$ .

$\frac{5}{3} \cdot (3 (2)) + b = 6$

Cancel the common factor.

$\frac{5}{3} \cdot (3 \cdot 2) + b = 6$

Rewrite the expression.

$5 \cdot 2 + b = 6$

Multiply $5$ by $2$ .

$10 + b = 6$

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

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Subtract $10$ from both sides of the equation.

$b = 6 - 10$

Subtract $10$ from $6$ .

$b = - 4$

List the slope and y-intercept.

Slope: $\frac{5}{3}$

y-intercept: $(0, - 4)$