Pre-Algebra Examples

$(- 7, - 4)$ AND, $(8, 8)$

Step 1

Find the slope of the line between $(- 7, - 4)$ and $(8, 8)$ using $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ , which is the change of $y$ over the change of $x$ .

Tap for more steps...

Step 1.1

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 1.2

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 1.3

Substitute in the values of $x$ and $y$ into the equation to find the slope.

$m = \frac{8 - (- 4)}{8 - (- 7)}$

Step 1.4

Simplify.

Tap for more steps...

Step 1.4.1

Simplify the numerator.

Tap for more steps...

Step 1.4.1.1

Multiply $- 1$ by $- 4$ .

$m = \frac{8 + 4}{8 - (- 7)}$

Step 1.4.1.2

Add $8$ and $4$ .

$m = \frac{12}{8 - (- 7)}$

Step 1.4.2

Simplify the denominator.

Tap for more steps...

Step 1.4.2.1

Multiply $- 1$ by $- 7$ .

$m = \frac{12}{8 + 7}$

Step 1.4.2.2

Add $8$ and $7$ .

$m = \frac{12}{15}$

Step 1.4.3

Cancel the common factor of $12$ and $15$ .

Tap for more steps...

Step 1.4.3.1

Factor $3$ out of $12$ .

$m = \frac{3 (4)}{15}$

Step 1.4.3.2

Cancel the common factors.

Tap for more steps...

Step 1.4.3.2.1

Factor $3$ out of $15$ .

$m = \frac{3 \cdot 4}{3 \cdot 5}$

Step 1.4.3.2.2

Cancel the common factor.

$m = \frac{3 \cdot 4}{3 \cdot 5}$

Step 1.4.3.2.3

Rewrite the expression.

$m = \frac{4}{5}$

Step 2

Use the slope $\frac{4}{5}$ and a given point $(- 7, - 4)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 4) = \frac{4}{5} \cdot (x - (- 7))$

Step 3

Simplify the equation and keep it in point-slope form.

$y + 4 = \frac{4}{5} \cdot (x + 7)$

Step 4

Solve for $y$ .

Tap for more steps...

Step 4.1

Simplify $\frac{4}{5} \cdot (x + 7)$ .

Tap for more steps...

Step 4.1.1

Rewrite.

$y + 4 = 0 + 0 + \frac{4}{5} \cdot (x + 7)$

Step 4.1.2

Simplify by adding zeros.

$y + 4 = \frac{4}{5} \cdot (x + 7)$

Step 4.1.3

Apply the distributive property.

$y + 4 = \frac{4}{5} x + \frac{4}{5} \cdot 7$

Step 4.1.4

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

$y + 4 = \frac{4 x}{5} + \frac{4}{5} \cdot 7$

Step 4.1.5

Multiply $\frac{4}{5} \cdot 7$ .

Tap for more steps...

Step 4.1.5.1

Combine $\frac{4}{5}$ and $7$ .

$y + 4 = \frac{4 x}{5} + \frac{4 \cdot 7}{5}$

Step 4.1.5.2

Multiply $4$ by $7$ .

$y + 4 = \frac{4 x}{5} + \frac{28}{5}$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Subtract $4$ from both sides of the equation.

$y = \frac{4 x}{5} + \frac{28}{5} - 4$

Step 4.2.2

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

$y = \frac{4 x}{5} + \frac{28}{5} - 4 \cdot \frac{5}{5}$

Step 4.2.3

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

$y = \frac{4 x}{5} + \frac{28}{5} + \frac{- 4 \cdot 5}{5}$

Step 4.2.4

Combine the numerators over the common denominator.

$y = \frac{4 x}{5} + \frac{28 - 4 \cdot 5}{5}$

Step 4.2.5

Simplify the numerator.

Tap for more steps...

Step 4.2.5.1

Multiply $- 4$ by $5$ .

$y = \frac{4 x}{5} + \frac{28 - 20}{5}$

Step 4.2.5.2

Subtract $20$ from $28$ .

$y = \frac{4 x}{5} + \frac{8}{5}$

Step 5

Reorder terms.

$y = \frac{4}{5} x + \frac{8}{5}$

Step 6

List the equation in different forms.

Slope-intercept form:

$y = \frac{4}{5} x + \frac{8}{5}$

Point-slope form:

$y + 4 = \frac{4}{5} \cdot (x + 7)$

Step 7