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

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

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

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

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

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

Solve for $y$ .

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

Rewrite.

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

Simplify by adding zeros.

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

Apply the distributive property.

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

Combine $\frac{1}{5}$ and $x$ .

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

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Subtract $1$ from both sides of the equation.

$y = \frac{x}{5} - 1 - 1$

Subtract $1$ from $- 1$ .

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

Reorder terms.

$y = \frac{1}{5} x - 2$

List the equation in different forms.

Slope-intercept form:

$y = \frac{1}{5} x - 2$

Point-slope form:

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

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

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