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Precalculus Examples

(- 5, - 7)

$(- 5, - 7)$ ,

12

$12$

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 + 12

$y = m x + 12$

Step 3

Substitute the value of

x

$x$ into the equation.

y = m (- 5) + 12

$y = m (- 5) + 12$

Step 4

Substitute the value of

y

$y$ into the equation.

- 7 = m (- 5) + 12

$- 7 = m (- 5) + 12$

Step 5

Find the value of

m

$m$ .

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Step 5.1

Rewrite the equation as

m (- 5) + 12 = - 7

$m (- 5) + 12 = - 7$ .

m (- 5) + 12 = - 7

$m (- 5) + 12 = - 7$

Step 5.2

Move

- 5

$- 5$ to the left of

m

$m$ .

- 5 m + 12 = - 7

$- 5 m + 12 = - 7$

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

12

$12$ from both sides of the equation.

- 5 m = - 7 - 12

$- 5 m = - 7 - 12$

Step 5.3.2

Subtract

12

$12$ from

- 7

$- 7$ .

- 5 m = - 19

$- 5 m = - 19$

- 5 m = - 19

$- 5 m = - 19$

Step 5.4

Divide each term in

- 5 m = - 19

$- 5 m = - 19$ by

- 5

$- 5$ and simplify.

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Step 5.4.1

Divide each term in

- 5 m = - 19

$- 5 m = - 19$ by

- 5

$- 5$ .

\frac{- 5 m}{- 5} = \frac{- 19}{- 5}

$\frac{- 5 m}{- 5} = \frac{- 19}{- 5}$

Step 5.4.2

Simplify the left side.

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Step 5.4.2.1

Cancel the common factor of

- 5

$- 5$ .

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Step 5.4.2.1.1

Cancel the common factor.

\frac{- 5 m}{- 5} = \frac{- 19}{- 5}

$\frac{- 5 m}{- 5} = \frac{- 19}{- 5}$

Step 5.4.2.1.2

Divide

m

$m$ by

1

$1$ .

m = \frac{- 19}{- 5}

$m = \frac{- 19}{- 5}$

m = \frac{- 19}{- 5}

$m = \frac{- 19}{- 5}$

m = \frac{- 19}{- 5}

$m = \frac{- 19}{- 5}$

Step 5.4.3

Simplify the right side.

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Step 5.4.3.1

Dividing two negative values results in a positive value.

m = \frac{19}{5}

$m = \frac{19}{5}$

m = \frac{19}{5}

$m = \frac{19}{5}$

m = \frac{19}{5}

$m = \frac{19}{5}$

m = \frac{19}{5}

$m = \frac{19}{5}$

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{19}{5} x + 12

$y = \frac{19}{5} x + 12$

Step 7

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

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