Precalculus Examples

$(4, \frac{π}{2})$ , $(8, 0)$

Step 1

Use $y = m x + b$ to calculate the equation of the line, where $m$ represents the slope and $b$ represents the y-intercept.

To calculate the equation of the line, use the $y = m x + b$ format.

Step 2

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 3

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 4

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

$m = \frac{0 - (\frac{π}{2})}{8 - (4)}$

Step 5

Finding the slope $m$ .

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Step 5.1

Multiply the numerator and denominator of the fraction by $2$ .

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Step 5.1.1

Multiply $\frac{0 - \frac{π}{2}}{8 - (4)}$ by $\frac{2}{2}$ .

$m = \frac{2}{2} \cdot \frac{0 - \frac{π}{2}}{8 - (4)}$

Step 5.1.2

Combine.

$m = \frac{2 (0 - \frac{π}{2})}{2 (8 - (4))}$

Step 5.2

Apply the distributive property.

$m = \frac{2 \cdot 0 + 2 (- \frac{π}{2})}{2 \cdot 8 + 2 (- (4))}$

Step 5.3

Cancel the common factor of $2$ .

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Step 5.3.1

Move the leading negative in $- \frac{π}{2}$ into the numerator.

$m = \frac{2 \cdot 0 + 2 (\frac{- π}{2})}{2 \cdot 8 + 2 (- (4))}$

Step 5.3.2

Cancel the common factor.

$m = \frac{2 \cdot 0 + 2 (\frac{- π}{2})}{2 \cdot 8 + 2 (- (4))}$

Step 5.3.3

Rewrite the expression.

$m = \frac{2 \cdot 0 - π}{2 \cdot 8 + 2 (- (4))}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Multiply $2$ by $0$ .

$m = \frac{0 - π}{2 \cdot 8 + 2 (- (4))}$

Step 5.4.2

Subtract $π$ from $0$ .

$m = \frac{- π}{2 \cdot 8 + 2 (- (4))}$

Step 5.5

Simplify the denominator.

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Step 5.5.1

Multiply $2$ by $8$ .

$m = \frac{- π}{16 + 2 (- (4))}$

Step 5.5.2

Multiply $2 (- (4))$ .

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Step 5.5.2.1

Multiply $- 1$ by $4$ .

$m = \frac{- π}{16 + 2 \cdot - 4}$

Step 5.5.2.2

Multiply $2$ by $- 4$ .

$m = \frac{- π}{16 - 8}$

Step 5.5.3

Subtract $8$ from $16$ .

$m = \frac{- π}{8}$

Step 5.6

Move the negative in front of the fraction.

$m = - \frac{π}{8}$

Step 6

Find the value of $b$ using the formula for the equation of a line.

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Step 6.1

Use the formula for the equation of a line to find $b$ .

$y = m x + b$

Step 6.2

Substitute the value of $m$ into the equation.

$y = (- \frac{π}{8}) \cdot x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (- \frac{π}{8}) \cdot (4) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$\frac{π}{2} = (- \frac{π}{8}) \cdot (4) + b$

Step 6.5

Find the value of $b$ .

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Step 6.5.1

Rewrite the equation as $- \frac{π}{8} \cdot 4 + b = \frac{π}{2}$ .

$- \frac{π}{8} \cdot 4 + b = \frac{π}{2}$

Step 6.5.2

Simplify each term.

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Step 6.5.2.1

Cancel the common factor of $4$ .

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Step 6.5.2.1.1

Move the leading negative in $- \frac{π}{8}$ into the numerator.

$\frac{- π}{8} \cdot 4 + b = \frac{π}{2}$

Step 6.5.2.1.2

Factor $4$ out of $8$ .

$\frac{- π}{4 (2)} \cdot 4 + b = \frac{π}{2}$

Step 6.5.2.1.3

Cancel the common factor.

$\frac{- π}{4 \cdot 2} \cdot 4 + b = \frac{π}{2}$

Step 6.5.2.1.4

Rewrite the expression.

$\frac{- π}{2} + b = \frac{π}{2}$

Step 6.5.2.2

Move the negative in front of the fraction.

$- \frac{π}{2} + b = \frac{π}{2}$

Step 6.5.3

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

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Step 6.5.3.1

Add $\frac{π}{2}$ to both sides of the equation.

$b = \frac{π}{2} + \frac{π}{2}$

Step 6.5.3.2

Combine the numerators over the common denominator.

$b = \frac{π + π}{2}$

Step 6.5.3.3

Add $π$ and $π$ .

$b = \frac{2 π}{2}$

Step 6.5.3.4

Cancel the common factor of $2$ .

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Step 6.5.3.4.1

Cancel the common factor.

$b = \frac{2 π}{2}$

Step 6.5.3.4.2

Divide $π$ by $1$ .

$b = π$

Step 7

Now that the values of $m$ (slope) and $b$ (y-intercept) are known, substitute them into $y = m x + b$ to find the equation of the line.

$y = - \frac{π}{8} x + π$

Step 8