Find the Slope (5/8,-3) , (-1/4,-1/4)

$(\frac{5}{8}, - 3)$ , $(- \frac{1}{4}, - \frac{1}{4})$

Step 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 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 3

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

$m = \frac{- \frac{1}{4} - (- 3)}{- \frac{1}{4} - (\frac{5}{8})}$

Step 4

Simplify.

Multiply the numerator and denominator of the complex fraction by $8$ .

Multiply $\frac{- \frac{1}{4} - (- 3)}{- \frac{1}{4} - \frac{5}{8}}$ by $\frac{8}{8}$ .

$m = \frac{8}{8} \cdot \frac{- \frac{1}{4} - (- 3)}{- \frac{1}{4} - \frac{5}{8}}$

Combine.

$m = \frac{8 (- \frac{1}{4} - (- 3))}{8 (- \frac{1}{4} - \frac{5}{8})}$

Apply the distributive property.

$m = \frac{8 (- \frac{1}{4}) + 8 (- (- 3))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Simplify by cancelling.

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$m = \frac{8 (\frac{- 1}{4}) + 8 (- (- 3))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Factor $4$ out of $8$ .

$m = \frac{4 (2) (\frac{- 1}{4}) + 8 (- (- 3))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Cancel the common factor.

$m = \frac{4 \cdot (2 (\frac{- 1}{4})) + 8 (- (- 3))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Rewrite the expression.

$m = \frac{2 \cdot - 1 + 8 (- (- 3))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Multiply $2$ by $- 1$ .

$m = \frac{- 2 + 8 (- (- 3))}{8 (- \frac{1}{4}) + 8 (- \frac{5}{8})}$

Cancel the common factor of $4$ .

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$m = \frac{- 2 + 8 (- (- 3))}{8 (\frac{- 1}{4}) + 8 (- \frac{5}{8})}$

Factor $4$ out of $8$ .

$m = \frac{- 2 + 8 (- (- 3))}{4 (2) (\frac{- 1}{4}) + 8 (- \frac{5}{8})}$

Cancel the common factor.

$m = \frac{- 2 + 8 (- (- 3))}{4 \cdot (2 (\frac{- 1}{4})) + 8 (- \frac{5}{8})}$

Rewrite the expression.

$m = \frac{- 2 + 8 (- (- 3))}{2 \cdot - 1 + 8 (- \frac{5}{8})}$

Multiply $2$ by $- 1$ .

$m = \frac{- 2 + 8 (- (- 3))}{- 2 + 8 (- \frac{5}{8})}$

Cancel the common factor of $8$ .

Move the leading negative in $- \frac{5}{8}$ into the numerator.

$m = \frac{- 2 + 8 (- (- 3))}{- 2 + 8 (\frac{- 5}{8})}$

Cancel the common factor.

$m = \frac{- 2 + 8 (- (- 3))}{- 2 + 8 (\frac{- 5}{8})}$

Rewrite the expression.

$m = \frac{- 2 + 8 (- (- 3))}{- 2 - 5}$

Simplify the numerator.

Multiply $8 (- (- 3))$ .

Multiply $- 1$ by $- 3$ .

$m = \frac{- 2 + 8 \cdot 3}{- 2 - 5}$

Multiply $8$ by $3$ .

$m = \frac{- 2 + 24}{- 2 - 5}$

Add $- 2$ and $24$ .

$m = \frac{22}{- 2 - 5}$

Simplify the expression.

Subtract $5$ from $- 2$ .

$m = \frac{22}{- 7}$

Move the negative in front of the fraction.

$m = - \frac{22}{7}$

Step 5

Find the Slope (5/8,-3) , (-1/4,-1/4)

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