Find the Equation Using Point-Slope Formula (-3,-5) ; m=-2/5

$(- 3, - 5)$ ; $m = - \frac{2}{5}$

Step 1

Use the slope $- \frac{2}{5}$ and a given point $(- 3, - 5)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 5) = - \frac{2}{5} \cdot (x - (- 3))$

Step 2

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

$y + 5 = - \frac{2}{5} \cdot (x + 3)$

Step 3

Solve for $y$ .

Simplify $- \frac{2}{5} \cdot (x + 3)$ .

Rewrite.

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

Simplify by adding zeros.

$y + 5 = - \frac{2}{5} \cdot (x + 3)$

Apply the distributive property.

$y + 5 = - \frac{2}{5} x - \frac{2}{5} \cdot 3$

Combine $x$ and $\frac{2}{5}$ .

$y + 5 = - \frac{x \cdot 2}{5} - \frac{2}{5} \cdot 3$

Multiply $- \frac{2}{5} \cdot 3$ .

Multiply $3$ by $- 1$ .

$y + 5 = - \frac{x \cdot 2}{5} - 3 (\frac{2}{5})$

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

$y + 5 = - \frac{x \cdot 2}{5} + \frac{- 3 \cdot 2}{5}$

Multiply $- 3$ by $2$ .

$y + 5 = - \frac{x \cdot 2}{5} + \frac{- 6}{5}$

Simplify each term.

Move $2$ to the left of $x$ .

$y + 5 = - \frac{2 \cdot x}{5} + \frac{- 6}{5}$

Move the negative in front of the fraction.

$y + 5 = - \frac{2 x}{5} - \frac{6}{5}$

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

Subtract $5$ from both sides of the equation.

$y = - \frac{2 x}{5} - \frac{6}{5} - 5$

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

$y = - \frac{2 x}{5} - \frac{6}{5} - 5 \cdot \frac{5}{5}$

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

$y = - \frac{2 x}{5} - \frac{6}{5} + \frac{- 5 \cdot 5}{5}$

Combine the numerators over the common denominator.

$y = - \frac{2 x}{5} + \frac{- 6 - 5 \cdot 5}{5}$

Simplify the numerator.

Multiply $- 5$ by $5$ .

$y = - \frac{2 x}{5} + \frac{- 6 - 25}{5}$

Subtract $25$ from $- 6$ .

$y = - \frac{2 x}{5} + \frac{- 31}{5}$

Move the negative in front of the fraction.

$y = - \frac{2 x}{5} - \frac{31}{5}$

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

Reorder terms.

$y = - (\frac{2}{5} x) - \frac{31}{5}$

Remove parentheses.

$y = - \frac{2}{5} x - \frac{31}{5}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - \frac{2}{5} x - \frac{31}{5}$

Point-slope form:

$y + 5 = - \frac{2}{5} \cdot (x + 3)$

Step 5

Find the Equation Using Point-Slope Formula (-3,-5) ; m=-2/5

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