Finite Math Examples

$(- 16, - 4)$ , $(4, - 16)$

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.

$m = \frac{- 16 - (- 4)}{4 - (- 16)}$

Step 5

Finding the slope $m$ .

Tap for more steps...

Step 5.1

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 5.1.1

Cancel the common factor of $- 16 - (- 4)$ and $4 - (- 16)$ .

Tap for more steps...

Step 5.1.1.1

Rewrite $- 16$ as $- 1 (16)$ .

$m = \frac{- 1 \cdot 16 - (- 4)}{4 - (- 16)}$

Step 5.1.1.2

Factor $- 1$ out of $- 1 (16) - (- 4)$ .

$m = \frac{- 1 (16 - 4)}{4 - (- 16)}$

Step 5.1.1.3

Reorder terms.

$m = \frac{- 1 (16 - 4)}{4 - 16 \cdot - 1}$

Step 5.1.1.4

Factor $4$ out of $- 1 (16 - 4)$ .

$m = \frac{4 (- 1 (4 - 1))}{4 - 16 \cdot - 1}$

Step 5.1.1.5

Cancel the common factors.

Tap for more steps...

Step 5.1.1.5.1

Factor $4$ out of $4$ .

$m = \frac{4 (- 1 (4 - 1))}{4 (1) - 16 \cdot - 1}$

Step 5.1.1.5.2

Factor $4$ out of $- 16 \cdot - 1$ .

$m = \frac{4 (- 1 (4 - 1))}{4 (1) + 4 (- 4 \cdot - 1)}$

Step 5.1.1.5.3

Factor $4$ out of $4 (1) + 4 (- 4 \cdot - 1)$ .

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

Step 5.1.1.5.4

Cancel the common factor.

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

Step 5.1.1.5.5

Rewrite the expression.

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

Step 5.1.2

Subtract $1$ from $4$ .

$m = \frac{- 1 \cdot 3}{1 - 4 \cdot - 1}$

Step 5.2

Simplify the denominator.

Tap for more steps...

Step 5.2.1

Multiply $- 4$ by $- 1$ .

$m = \frac{- 1 \cdot 3}{1 + 4}$

Step 5.2.2

Add $1$ and $4$ .

$m = \frac{- 1 \cdot 3}{5}$

Step 5.3

Simplify the expression.

Tap for more steps...

Step 5.3.1

Multiply $- 1$ by $3$ .

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

Step 5.3.2

Move the negative in front of the fraction.

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

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.

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

Step 6.3

Substitute the value of $x$ into the equation.

$y = (- \frac{3}{5}) \cdot (- 16) + b$

Step 6.4

Substitute the value of $y$ into the equation.

$- 4 = (- \frac{3}{5}) \cdot (- 16) + b$

Step 6.5

Find the value of $b$ .

Tap for more steps...

Step 6.5.1

Rewrite the equation as $- \frac{3}{5} \cdot - 16 + b = - 4$ .

$- \frac{3}{5} \cdot - 16 + b = - 4$

Step 6.5.2

Multiply $- \frac{3}{5} \cdot - 16$ .

Tap for more steps...

Step 6.5.2.1

Multiply $- 16$ by $- 1$ .

$16 (\frac{3}{5}) + b = - 4$

Step 6.5.2.2

Combine $16$ and $\frac{3}{5}$ .

$\frac{16 \cdot 3}{5} + b = - 4$

Step 6.5.2.3

Multiply $16$ by $3$ .

$\frac{48}{5} + b = - 4$

Step 6.5.3

Move all terms not containing $b$ to the right side of the equation.

Tap for more steps...

Step 6.5.3.1

Subtract $\frac{48}{5}$ from both sides of the equation.

$b = - 4 - \frac{48}{5}$

Step 6.5.3.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$b = - 4 \cdot \frac{5}{5} - \frac{48}{5}$

Step 6.5.3.3

Combine $- 4$ and $\frac{5}{5}$ .

$b = \frac{- 4 \cdot 5}{5} - \frac{48}{5}$

Step 6.5.3.4

Combine the numerators over the common denominator.

$b = \frac{- 4 \cdot 5 - 48}{5}$

Step 6.5.3.5

Simplify the numerator.

Tap for more steps...

Step 6.5.3.5.1

Multiply $- 4$ by $5$ .

$b = \frac{- 20 - 48}{5}$

Step 6.5.3.5.2

Subtract $48$ from $- 20$ .

$b = \frac{- 68}{5}$

Step 6.5.3.6

Move the negative in front of the fraction.

$b = - \frac{68}{5}$

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.

$y = - \frac{3}{5} x - \frac{68}{5}$

Step 8