Algebra Examples

$(1, 2)$ ,

$(3, 4)$

Step 1

Use

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

$m$ represents the slope and

$b$ represents the y-intercept.

To calculate the equation of the line, use the

$y = m x + b$ format.

Step 2

Slope is equal to the change in

$y$ over the change in

$x$ , or rise over run.

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

Step 3

The change in

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

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

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

Step 4

Substitute in the values of

$x$ and

$y$ into the equation to find the slope.

$m = \frac{4 - (2)}{3 - (1)}$

Step 5

Finding the slope

$m$ .

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply

$- 1$ by

$2$ .

$m = \frac{4 - 2}{3 - (1)}$

Step 5.1.2

Subtract

$2$ from

$4$ .

$m = \frac{2}{3 - (1)}$

Step 5.2

Simplify the denominator.

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Step 5.2.1

Multiply

$- 1$ by

$1$ .

$m = \frac{2}{3 - 1}$

Step 5.2.2

Subtract

$1$ from

$3$ .

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

Step 5.3

Divide

$2$ by

$2$ .

$m = 1$

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.

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

Step 6.4

Substitute the value of

$y$ into the equation.

$2 = (1) \cdot (1) + b$

Step 6.5

Find the value of

$b$ .

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Step 6.5.1

Rewrite the equation as

$(1) \cdot (1) + b = 2$ .

$(1) \cdot (1) + b = 2$

Step 6.5.2

Multiply

$1$ by

$1$ .

$1 + b = 2$

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

$1$ from both sides of the equation.

$b = 2 - 1$

Step 6.5.3.2

Subtract

$1$ from

$2$ .

$b = 1$

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.

$y = x + 1$

Step 8

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