Algebra Examples

(0, 3)

$(0, 3)$ ,

(2, 0)

$(2, 0)$

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 - (3)}{2 - (0)}

$m = \frac{0 - (3)}{2 - (0)}$

Step 5

Finding the slope

m

$m$ .

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply

- 1

$- 1$ by

3

$3$ .

m = \frac{0 - 3}{2 - (0)}

$m = \frac{0 - 3}{2 - (0)}$

Step 5.1.2

Subtract

3

$3$ from

0

$0$ .

m = \frac{- 3}{2 - (0)}

$m = \frac{- 3}{2 - (0)}$

m = \frac{- 3}{2 - (0)}

$m = \frac{- 3}{2 - (0)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply

- 1

$- 1$ by

0

$0$ .

m = \frac{- 3}{2 + 0}

$m = \frac{- 3}{2 + 0}$

Step 5.2.2

Add

2

$2$ and

0

$0$ .

m = \frac{- 3}{2}

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

m = \frac{- 3}{2}

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

Step 5.3

Move the negative in front of the fraction.

m = - \frac{3}{2}

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

m = - \frac{3}{2}

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

Step 6

Find the value of

b

$b$ 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

$b$ .

y = m x + b

$y = m x + b$

Step 6.2

Substitute the value of

m

$m$ into the equation.

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

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

Step 6.3

Substitute the value of

x

$x$ into the equation.

y = (- \frac{3}{2}) \cdot (0) + b

$y = (- \frac{3}{2}) \cdot (0) + b$

Step 6.4

Substitute the value of

y

$y$ into the equation.

3 = (- \frac{3}{2}) \cdot (0) + b

$3 = (- \frac{3}{2}) \cdot (0) + b$

Step 6.5

Find the value of

b

$b$ .

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Step 6.5.1

Rewrite the equation as

- \frac{3}{2} \cdot 0 + b = 3

$- \frac{3}{2} \cdot 0 + b = 3$ .

- \frac{3}{2} \cdot 0 + b = 3

$- \frac{3}{2} \cdot 0 + b = 3$

Step 6.5.2

Simplify

- \frac{3}{2} \cdot 0 + b

$- \frac{3}{2} \cdot 0 + b$ .

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Step 6.5.2.1

Multiply

$- \frac{3}{2} \cdot 0$ .

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Step 6.5.2.1.1

Multiply

$0$ by

$- 1$ .

$0 (\frac{3}{2}) + b = 3$

Step 6.5.2.1.2

Multiply

$0$ by

$\frac{3}{2}$ .

$0 + b = 3$

Step 6.5.2.2

Add

$0$ and

$b$ .

$b = 3$

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.

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

Step 8