Find the Equation Using Point-Slope Formula m=-1/2 , (-5,0)

$m = - \frac{1}{2}$ , $(- 5, 0)$

Step 1

Use the slope $- \frac{1}{2}$ and a given point $(- 5, 0)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (0) = - \frac{1}{2} \cdot (x - (- 5))$

Step 2

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

$y + 0 = - \frac{1}{2} \cdot (x + 5)$

Step 3

Solve for $y$ .

Add $y$ and $0$ .

$y = - \frac{1}{2} \cdot (x + 5)$

Simplify $- \frac{1}{2} \cdot (x + 5)$ .

Apply the distributive property.

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

Combine $x$ and $\frac{1}{2}$ .

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

Multiply $- \frac{1}{2} \cdot 5$ .

Multiply $5$ by $- 1$ .

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

Combine $- 5$ and $\frac{1}{2}$ .

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

Move the negative in front of the fraction.

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

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

Reorder terms.

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

Remove parentheses.

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

Step 4

List the equation in different forms.

Slope-intercept form:

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

Point-slope form:

$y + 0 = - \frac{1}{2} \cdot (x + 5)$

Step 5

Find the Equation Using Point-Slope Formula m=-1/2 , (-5,0)

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