Find the Equation Using Point-Slope Formula m=3/5 ; (-1,4)

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

Step 1

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

$y - (4) = \frac{3}{5} \cdot (x - (- 1))$

Step 2

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

$y - 4 = \frac{3}{5} \cdot (x + 1)$

Step 3

Solve for $y$ .

Simplify $\frac{3}{5} \cdot (x + 1)$ .

Rewrite.

$y - 4 = 0 + 0 + \frac{3}{5} \cdot (x + 1)$

Simplify by adding zeros.

$y - 4 = \frac{3}{5} \cdot (x + 1)$

Apply the distributive property.

$y - 4 = \frac{3}{5} x + \frac{3}{5} \cdot 1$

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

$y - 4 = \frac{3 x}{5} + \frac{3}{5} \cdot 1$

Multiply $\frac{3}{5}$ by $1$ .

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

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

Add $4$ to both sides of the equation.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $4$ by $5$ .

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

Add $3$ and $20$ .

$y = \frac{3 x}{5} + \frac{23}{5}$

Reorder terms.

$y = \frac{3}{5} x + \frac{23}{5}$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = \frac{3}{5} x + \frac{23}{5}$

Point-slope form:

$y - 4 = \frac{3}{5} \cdot (x + 1)$

Step 5

Find the Equation Using Point-Slope Formula m=3/5 ; (-1,4)

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