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Precalculus Examples

(2, 3)

$(2, 3)$ ,

b = 6

$b = 6$

Step 1

Find the value of

m

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

y = m x + b

$y = m x + b$

Step 2

Substitute the value of

b

$b$ into the equation.

y = m x + 6

$y = m x + 6$

Step 3

Substitute the value of

x

$x$ into the equation.

y = m (2) + 6

$y = m (2) + 6$

Step 4

Substitute the value of

y

$y$ into the equation.

3 = m (2) + 6

$3 = m (2) + 6$

Step 5

Find the value of

m

$m$ .

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Step 5.1

Rewrite the equation as

m (2) + 6 = 3

$m (2) + 6 = 3$ .

m (2) + 6 = 3

$m (2) + 6 = 3$

Step 5.2

Move

2

$2$ to the left of

m

$m$ .

2 m + 6 = 3

$2 m + 6 = 3$

Step 5.3

Move all terms not containing

m

$m$ to the right side of the equation.

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Step 5.3.1

Subtract

6

$6$ from both sides of the equation.

2 m = 3 - 6

$2 m = 3 - 6$

Step 5.3.2

Subtract

6

$6$ from

3

$3$ .

2 m = - 3

$2 m = - 3$

2 m = - 3

$2 m = - 3$

Step 5.4

Divide each term in

2 m = - 3

$2 m = - 3$ by

2

$2$ and simplify.

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Step 5.4.1

Divide each term in

2 m = - 3

$2 m = - 3$ by

2

$2$ .

\frac{2 m}{2} = \frac{- 3}{2}

$\frac{2 m}{2} = \frac{- 3}{2}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of

2

$2$ .

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Step 5.4.2.1.1

Cancel the common factor.

\frac{2 m}{2} = \frac{- 3}{2}

$\frac{2 m}{2} = \frac{- 3}{2}$

Step 5.4.2.1.2

Divide

m

$m$ by

1

$1$ .

m = \frac{- 3}{2}

$m = \frac{- 3}{2}$

m = \frac{- 3}{2}

$m = \frac{- 3}{2}$

m = \frac{- 3}{2}

$m = \frac{- 3}{2}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Move the negative in front of the fraction.

m = - \frac{3}{2}

$m = - \frac{3}{2}$

m = - \frac{3}{2}

$m = - \frac{3}{2}$

m = - \frac{3}{2}

$m = - \frac{3}{2}$

m = - \frac{3}{2}

$m = - \frac{3}{2}$

Step 6

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{3}{2} x + 6

$y = - \frac{3}{2} x + 6$

Step 7

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

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