Find the Equation Using Point-Slope Formula (-8,6) , slope=1/4

$(- 8, 6)$ , $s l o p e = \frac{1}{4}$

Step 1

Use the slope $\frac{1}{4}$ and a given point $(- 8, 6)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (6) = \frac{1}{4} \cdot (x - (- 8))$

Step 2

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

$y - 6 = \frac{1}{4} \cdot (x + 8)$

Step 3

Solve for $y$ .

Simplify $\frac{1}{4} \cdot (x + 8)$ .

Rewrite.

$y - 6 = 0 + 0 + \frac{1}{4} \cdot (x + 8)$

Simplify by adding zeros.

$y - 6 = \frac{1}{4} \cdot (x + 8)$

Apply the distributive property.

$y - 6 = \frac{1}{4} x + \frac{1}{4} \cdot 8$

Combine $\frac{1}{4}$ and $x$ .

$y - 6 = \frac{x}{4} + \frac{1}{4} \cdot 8$

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$y - 6 = \frac{x}{4} + \frac{1}{4} \cdot (4 (2))$

Cancel the common factor.

$y - 6 = \frac{x}{4} + \frac{1}{4} \cdot (4 \cdot 2)$

Rewrite the expression.

$y - 6 = \frac{x}{4} + 2$

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

Add $6$ to both sides of the equation.

$y = \frac{x}{4} + 2 + 6$

Add $2$ and $6$ .

$y = \frac{x}{4} + 8$

Reorder terms.

$y = \frac{1}{4} x + 8$

Step 4

List the equation in different forms.

Slope-intercept form:

$y = \frac{1}{4} x + 8$

Point-slope form:

$y - 6 = \frac{1}{4} \cdot (x + 8)$

Step 5

Find the Equation Using Point-Slope Formula (-8,6) , slope=1/4

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