Find the Equation Using Point-Slope Formula (-10,-6) ; m=-5/8

$(- 10, - 6)$ ; $m = - \frac{5}{8}$

Step 1

Use the slope $- \frac{5}{8}$ and a given point $(- 10, - 6)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 6) = - \frac{5}{8} \cdot (x - (- 10))$

Step 2

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

$y + 6 = - \frac{5}{8} \cdot (x + 10)$

Step 3

Solve for $y$ .

Simplify $- \frac{5}{8} \cdot (x + 10)$ .

Rewrite.

$y + 6 = 0 + 0 - \frac{5}{8} \cdot (x + 10)$

Simplify terms.

Apply the distributive property.

$y + 6 = - \frac{5}{8} x - \frac{5}{8} \cdot 10$

Combine $x$ and $\frac{5}{8}$ .

$y + 6 = - \frac{x \cdot 5}{8} - \frac{5}{8} \cdot 10$

Cancel the common factor of $2$ .

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

$y + 6 = - \frac{x \cdot 5}{8} + \frac{- 5}{8} \cdot 10$

Factor $2$ out of $8$ .

$y + 6 = - \frac{x \cdot 5}{8} + \frac{- 5}{2 (4)} \cdot 10$

Factor $2$ out of $10$ .

$y + 6 = - \frac{x \cdot 5}{8} + \frac{- 5}{2 \cdot 4} \cdot (2 \cdot 5)$

Cancel the common factor.

$y + 6 = - \frac{x \cdot 5}{8} + \frac{- 5}{2 \cdot 4} \cdot (2 \cdot 5)$

Rewrite the expression.

$y + 6 = - \frac{x \cdot 5}{8} + \frac{- 5}{4} \cdot 5$

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

$y + 6 = - \frac{x \cdot 5}{8} + \frac{- 5 \cdot 5}{4}$

Multiply $- 5$ by $5$ .

$y + 6 = - \frac{x \cdot 5}{8} + \frac{- 25}{4}$

Simplify each term.

Move $5$ to the left of $x$ .

$y + 6 = - \frac{5 \cdot x}{8} + \frac{- 25}{4}$

Move the negative in front of the fraction.

$y + 6 = - \frac{5 x}{8} - \frac{25}{4}$

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

Subtract $6$ from both sides of the equation.

$y = - \frac{5 x}{8} - \frac{25}{4} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{5 x}{8} - \frac{25}{4} - 6 \cdot \frac{4}{4}$

Combine $- 6$ and $\frac{4}{4}$ .

$y = - \frac{5 x}{8} - \frac{25}{4} + \frac{- 6 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = - \frac{5 x}{8} + \frac{- 25 - 6 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 6$ by $4$ .

$y = - \frac{5 x}{8} + \frac{- 25 - 24}{4}$

Subtract $24$ from $- 25$ .

$y = - \frac{5 x}{8} + \frac{- 49}{4}$

Move the negative in front of the fraction.

$y = - \frac{5 x}{8} - \frac{49}{4}$

Write in $y = m x + b$ form.

Reorder terms.

$y = - (\frac{5}{8} x) - \frac{49}{4}$

Remove parentheses.

$y = - \frac{5}{8} x - \frac{49}{4}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - \frac{5}{8} x - \frac{49}{4}$

Point-slope form:

$y + 6 = - \frac{5}{8} \cdot (x + 10)$

Step 5

Find the Equation Using Point-Slope Formula (-10,-6) ; m=-5/8

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