Precalculus Examples

$(- 8, - 5)$ , $(0, - 6.14)$

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.

$m = \frac{- 6.14 - (- 5)}{0 - (- 8)}$

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 $- 5$ .

$m = \frac{- 6.14 + 5}{0 - (- 8)}$

Step 1.4.1.2

Add $- 6.14$ and $5$ .

$m = \frac{- 1.14}{0 - (- 8)}$

Step 1.4.2

Simplify the denominator.

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Step 1.4.2.1

Multiply $- 1$ by $- 8$ .

$m = \frac{- 1.14}{0 + 8}$

Step 1.4.2.2

Add $0$ and $8$ .

$m = \frac{- 1.14}{8}$

Step 1.4.3

Divide $- 1.14$ by $8$ .

$m = - 0.1425$

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, $y = m x + b$ .

$y = (- 0.1425) \cdot x + b$

Step 2.2

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

$y = (- 0.1425) \cdot (- 8) + b$

Step 2.3

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

$- 5 = (- 0.1425) \cdot (- 8) + b$

Step 2.4

Rewrite the equation as $(- 0.1425) \cdot (- 8) + b = - 5$ .

$(- 0.1425) \cdot (- 8) + b = - 5$

Step 2.5

Multiply $- 0.1425$ by $- 8$ .

$1.14 + b = - 5$

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 $1.14$ from both sides of the equation.

$b = - 5 - 1.14$

Step 2.6.2

Subtract $1.14$ from $- 5$ .

$b = - 6.14$

Step 3

List the slope and y-intercept.

Slope: $- 0.1425$

y-intercept: $(0, - 6.14)$

Step 4