Precalculus Examples

vertex

(4, 4)

$(4, 4)$ , point

(0, 0)

$(0, 0)$

Step 1

Use

y = m x + b

$y = m x + b$ to calculate the equation of the line, where

m

$m$ represents the slope and

b

$b$ represents the y-intercept.

To calculate the equation of the line, use the

y = m x + b

$y = m x + b$ format.

Step 2

Slope is equal to the change in

y

$y$ over the change in

x

$x$ , or rise over run.

m = \frac{(change in y)}{(change in x)}

$m = \frac{(change in y)}{(change in x)}$

Step 3

The change in

x

$x$ is equal to the difference in x-coordinates (also called run), and the change in

y

$y$ is equal to the difference in y-coordinates (also called rise).

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Step 4

Substitute in the values of

x

$x$ and

y

$y$ into the equation to find the slope.

m = \frac{0 - (4)}{0 - (4)}

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

Step 5

Cancel the common factor of

0 - (4)

$0 - (4)$ .

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Step 5.1

Cancel the common factor.

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

Step 5.2

Rewrite the expression.

$m = 1$

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.

$y = (1) \cdot x + b$

Step 6.3

Substitute the value of

$x$ into the equation.

$y = (1) \cdot (4) + b$

Step 6.4

Substitute the value of

$y$ into the equation.

$4 = (1) \cdot (4) + b$

Step 6.5

Find the value of

$b$ .

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Step 6.5.1

Rewrite the equation as

$(1) \cdot (4) + b = 4$ .

$(1) \cdot (4) + b = 4$

Step 6.5.2

Multiply

$4$ by

$1$ .

$4 + b = 4$

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

Subtract

$4$ from both sides of the equation.

$b = 4 - 4$

Step 6.5.3.2

Subtract

$4$ from

$4$ .

$b = 0$

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.

$y = x$

Step 8