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Precalculus Examples

(- 2, - 8)

$(- 2, - 8)$ ,

m = \frac{1}{3}

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

Step 1

Find the value of

b

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

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Step 1.1

Use the formula for the equation of a line to find

b

$b$ .

y = m x + b

$y = m x + b$

Step 1.2

Substitute the value of

m

$m$ into the equation.

y = (\frac{1}{3}) x + b

$y = (\frac{1}{3}) x + b$

Step 1.3

Substitute the value of

x

$x$ into the equation.

y = (\frac{1}{3}) \cdot (- 2) + b

$y = (\frac{1}{3}) \cdot (- 2) + b$

Step 1.4

Substitute the value of

y

$y$ into the equation.

- 8 = (\frac{1}{3}) \cdot (- 2) + b

$- 8 = (\frac{1}{3}) \cdot (- 2) + b$

Step 1.5

Find the value of

b

$b$ .

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Step 1.5.1

Rewrite the equation as

\frac{1}{3} \cdot - 2 + b = - 8

$\frac{1}{3} \cdot - 2 + b = - 8$ .

\frac{1}{3} \cdot - 2 + b = - 8

$\frac{1}{3} \cdot - 2 + b = - 8$

Step 1.5.2

Simplify each term.

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Step 1.5.2.1

Combine

\frac{1}{3}

$\frac{1}{3}$ and

- 2

$- 2$ .

\frac{- 2}{3} + b = - 8

$\frac{- 2}{3} + b = - 8$

Step 1.5.2.2

Move the negative in front of the fraction.

- \frac{2}{3} + b = - 8

$- \frac{2}{3} + b = - 8$

- \frac{2}{3} + b = - 8

$- \frac{2}{3} + b = - 8$

Step 1.5.3

Move all terms not containing

b

$b$ to the right side of the equation.

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Step 1.5.3.1

Add

\frac{2}{3}

$\frac{2}{3}$ to both sides of the equation.

b = - 8 + \frac{2}{3}

$b = - 8 + \frac{2}{3}$

Step 1.5.3.2

To write

- 8

$- 8$ as a fraction with a common denominator, multiply by

\frac{3}{3}

$\frac{3}{3}$ .

b = - 8 \cdot \frac{3}{3} + \frac{2}{3}

$b = - 8 \cdot \frac{3}{3} + \frac{2}{3}$

Step 1.5.3.3

Combine

- 8

$- 8$ and

\frac{3}{3}

$\frac{3}{3}$ .

b = \frac{- 8 \cdot 3}{3} + \frac{2}{3}

$b = \frac{- 8 \cdot 3}{3} + \frac{2}{3}$

Step 1.5.3.4

Combine the numerators over the common denominator.

b = \frac{- 8 \cdot 3 + 2}{3}

$b = \frac{- 8 \cdot 3 + 2}{3}$

Step 1.5.3.5

Simplify the numerator.

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Step 1.5.3.5.1

Multiply

- 8

$- 8$ by

3

$3$ .

b = \frac{- 24 + 2}{3}

$b = \frac{- 24 + 2}{3}$

Step 1.5.3.5.2

Add

- 24

$- 24$ and

2

$2$ .

b = \frac{- 22}{3}

$b = \frac{- 22}{3}$

b = \frac{- 22}{3}

$b = \frac{- 22}{3}$

Step 1.5.3.6

Move the negative in front of the fraction.

b = - \frac{22}{3}

$b = - \frac{22}{3}$

b = - \frac{22}{3}

$b = - \frac{22}{3}$

b = - \frac{22}{3}

$b = - \frac{22}{3}$

b = - \frac{22}{3}

$b = - \frac{22}{3}$

Step 2

Now that the values of

m

$m$ (slope) and

b

$b$ (y-intercept) are known, substitute them into

y = m x + b

$y = m x + b$ to find the equation of the line.

y = \frac{1}{3} x - \frac{22}{3}

$y = \frac{1}{3} x - \frac{22}{3}$

Step 3

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⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$