Finite Math Examples

$(- 4, 0)$ , $(6, 3)$

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.

$m = \frac{3 - (0)}{6 - (- 4)}$

Step 5

Finding the slope $m$ .

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Multiply $- 1$ by $0$ .

$m = \frac{3 + 0}{6 - (- 4)}$

Step 5.1.2

Add $3$ and $0$ .

$m = \frac{3}{6 - (- 4)}$

Step 5.2

Simplify the denominator.

Tap for more steps...

Step 5.2.1

Multiply $- 1$ by $- 4$ .

$m = \frac{3}{6 + 4}$

Step 5.2.2

Add $6$ and $4$ .

$m = \frac{3}{10}$

Step 6

Find the value of $b$ using the formula for the equation of a line.

Tap for more steps...

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.

$y = (\frac{3}{10}) x + b$

Step 6.3

Substitute the value of $x$ into the equation.

$y = (\frac{3}{10}) \cdot (- 4) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$0 = (\frac{3}{10}) \cdot (- 4) + b$

Step 6.5

Find the value of $b$ .

Tap for more steps...

Step 6.5.1

Rewrite the equation as $\frac{3}{10} \cdot - 4 + b = 0$ .

$\frac{3}{10} \cdot - 4 + b = 0$

Step 6.5.2

Simplify each term.

Tap for more steps...

Step 6.5.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.5.2.1.1

Factor $2$ out of $10$ .

$\frac{3}{2 (5)} \cdot - 4 + b = 0$

Step 6.5.2.1.2

Factor $2$ out of $- 4$ .

$\frac{3}{2 \cdot 5} \cdot (2 \cdot - 2) + b = 0$

Step 6.5.2.1.3

Cancel the common factor.

$\frac{3}{2 \cdot 5} \cdot (2 \cdot - 2) + b = 0$

Step 6.5.2.1.4

Rewrite the expression.

$\frac{3}{5} \cdot - 2 + b = 0$

Step 6.5.2.2

Combine $\frac{3}{5}$ and $- 2$ .

$\frac{3 \cdot - 2}{5} + b = 0$

Step 6.5.2.3

Multiply $3$ by $- 2$ .

$\frac{- 6}{5} + b = 0$

Step 6.5.2.4

Move the negative in front of the fraction.

$- \frac{6}{5} + b = 0$

Step 6.5.3

Add $\frac{6}{5}$ to both sides of the equation.

$b = \frac{6}{5}$

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.

$y = \frac{3}{10} x + \frac{6}{5}$

Step 8