Find the Equation Using Point-Slope Formula (-5,-3) , slope=-3/5

$(- 5, - 3)$ , $s l o p e = - \frac{3}{5}$

Step 1

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

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

Step 2

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

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

Step 3

Solve for $y$ .

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

Rewrite.

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

Simplify terms.

Apply the distributive property.

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

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

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

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{3}{5}$ into the numerator.

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

Cancel the common factor.

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

Rewrite the expression.

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

Move $3$ to the left of $x$ .

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

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

Subtract $3$ from both sides of the equation.

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

Subtract $3$ from $- 3$ .

$y = - \frac{3 x}{5} - 6$

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

Reorder terms.

$y = - (\frac{3}{5} x) - 6$

Remove parentheses.

$y = - \frac{3}{5} x - 6$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = - \frac{3}{5} x - 6$

Point-slope form:

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

Step 5

Find the Equation Using Point-Slope Formula (-5,-3) , slope=-3/5

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