Algebra Examples

$(4, 6)$ , $(- 1, 2)$

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.

$m = \frac{2 - (6)}{- 1 - (4)}$

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 $6$ .

$m = \frac{2 - 6}{- 1 - (4)}$

Step 1.4.1.2

Subtract $6$ from $2$ .

$m = \frac{- 4}{- 1 - (4)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $4$ .

$m = \frac{- 4}{- 1 - 4}$

Step 1.4.2.2

Subtract $4$ from $- 1$ .

$m = \frac{- 4}{- 5}$

Step 1.4.3

Dividing two negative values results in a positive value.

$m = \frac{4}{5}$

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, $y = m x + b$ .

$y = (\frac{4}{5}) x + b$

Step 2.2

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

$y = (\frac{4}{5}) \cdot (4) + b$

Step 2.3

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

$6 = (\frac{4}{5}) \cdot (4) + b$

Step 2.4

Rewrite the equation as $(\frac{4}{5}) \cdot (4) + b = 6$ .

$(\frac{4}{5}) \cdot (4) + b = 6$

Step 2.5

Multiply $(\frac{4}{5}) (4)$ .

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Step 2.5.1

Combine $\frac{4}{5}$ and $4$ .

$\frac{4 \cdot 4}{5} + b = 6$

Step 2.5.2

Multiply $4$ by $4$ .

$\frac{16}{5} + b = 6$

Step 2.6

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

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Step 2.6.1

Subtract $\frac{16}{5}$ from both sides of the equation.

$b = 6 - \frac{16}{5}$

Step 2.6.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = 6 \cdot \frac{5}{5} - \frac{16}{5}$

Step 2.6.3

Combine $6$ and $\frac{5}{5}$ .

$b = \frac{6 \cdot 5}{5} - \frac{16}{5}$

Step 2.6.4

Combine the numerators over the common denominator.

$b = \frac{6 \cdot 5 - 16}{5}$

Step 2.6.5

Simplify the numerator.

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Step 2.6.5.1

Multiply $6$ by $5$ .

$b = \frac{30 - 16}{5}$

Step 2.6.5.2

Subtract $16$ from $30$ .

$b = \frac{14}{5}$

Step 3

List the slope and y-intercept.

Slope: $\frac{4}{5}$

y-intercept: $(0, \frac{14}{5})$

Step 4