Algebra Examples

(0, 0)

$(0, 0)$ ,

(3, 5)

$(3, 5)$

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{5 - (0)}{3 - (0)}

$m = \frac{5 - (0)}{3 - (0)}$

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

0

$0$ .

m = \frac{5 + 0}{3 - (0)}

$m = \frac{5 + 0}{3 - (0)}$

Step 5.1.2

Add

5

$5$ and

0

$0$ .

m = \frac{5}{3 - (0)}

$m = \frac{5}{3 - (0)}$

m = \frac{5}{3 - (0)}

$m = \frac{5}{3 - (0)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply

- 1

$- 1$ by

0

$0$ .

m = \frac{5}{3 + 0}

$m = \frac{5}{3 + 0}$

Step 5.2.2

Add

3

$3$ and

0

$0$ .

m = \frac{5}{3}

$m = \frac{5}{3}$

m = \frac{5}{3}

$m = \frac{5}{3}$

m = \frac{5}{3}

$m = \frac{5}{3}$

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{5}{3}) x + b

$y = (\frac{5}{3}) x + b$

Step 6.3

Substitute the value of

x

$x$ into the equation.

y = (\frac{5}{3}) \cdot (0) + b

$y = (\frac{5}{3}) \cdot (0) + b$

Step 6.4

Substitute the value of

y

$y$ into the equation.

0 = (\frac{5}{3}) \cdot (0) + b

$0 = (\frac{5}{3}) \cdot (0) + b$

Step 6.5

Find the value of

b

$b$ .

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Step 6.5.1

Rewrite the equation as

\frac{5}{3} \cdot 0 + b = 0

$\frac{5}{3} \cdot 0 + b = 0$ .

\frac{5}{3} \cdot 0 + b = 0

$\frac{5}{3} \cdot 0 + b = 0$

Step 6.5.2

Simplify

\frac{5}{3} \cdot 0 + b

$\frac{5}{3} \cdot 0 + b$ .

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Step 6.5.2.1

Multiply

\frac{5}{3}

$\frac{5}{3}$ by

0

$0$ .

0 + b = 0

$0 + b = 0$

Step 6.5.2.2

Add

0

$0$ and

b

$b$ .

b = 0

$b = 0$

b = 0

$b = 0$

b = 0

$b = 0$

b = 0

$b = 0$

Step 7

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{5}{3} x

$y = \frac{5}{3} x$

Step 8