Find the Equation Using Point-Slope Formula m=3/5 and (2,-4)

$m = \frac{3}{5}$ and $(2, - 4)$

Step 1

Use the slope $\frac{3}{5}$ and a given point $(2, - 4)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 4) = \frac{3}{5} \cdot (x - (2))$

Step 2

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

$y + 4 = \frac{3}{5} \cdot (x - 2)$

Step 3

Solve for $y$ .

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

Rewrite.

$y + 4 = 0 + 0 + \frac{3}{5} \cdot (x - 2)$

Simplify by adding zeros.

$y + 4 = \frac{3}{5} \cdot (x - 2)$

Apply the distributive property.

$y + 4 = \frac{3}{5} x + \frac{3}{5} \cdot - 2$

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

$y + 4 = \frac{3 x}{5} + \frac{3}{5} \cdot - 2$

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

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

$y + 4 = \frac{3 x}{5} + \frac{3 \cdot - 2}{5}$

Multiply $3$ by $- 2$ .

$y + 4 = \frac{3 x}{5} + \frac{- 6}{5}$

Move the negative in front of the fraction.

$y + 4 = \frac{3 x}{5} - \frac{6}{5}$

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

Subtract $4$ from both sides of the equation.

$y = \frac{3 x}{5} - \frac{6}{5} - 4$

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

$y = \frac{3 x}{5} - \frac{6}{5} - 4 \cdot \frac{5}{5}$

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

$y = \frac{3 x}{5} - \frac{6}{5} + \frac{- 4 \cdot 5}{5}$

Combine the numerators over the common denominator.

$y = \frac{3 x}{5} + \frac{- 6 - 4 \cdot 5}{5}$

Simplify the numerator.

Multiply $- 4$ by $5$ .

$y = \frac{3 x}{5} + \frac{- 6 - 20}{5}$

Subtract $20$ from $- 6$ .

$y = \frac{3 x}{5} + \frac{- 26}{5}$

Move the negative in front of the fraction.

$y = \frac{3 x}{5} - \frac{26}{5}$

Reorder terms.

$y = \frac{3}{5} x - \frac{26}{5}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = \frac{3}{5} x - \frac{26}{5}$

Point-slope form:

$y + 4 = \frac{3}{5} \cdot (x - 2)$

Step 5

Find the Equation Using Point-Slope Formula m=3/5 and (2,-4)

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