Question

a line that includes the point (-6, 6) has a slope of $\frac{1}{4}$. what is its equation in point - slope form? use the specified point in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.

Explanation:

Step1: Recall point - slope formula

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.

Step2: Identify values of $x_1$, $y_1$ and $m$

Given the point $(-6,6)$ and slope $m = \frac{1}{4}$, so $x_1=-6$, $y_1 = 6$.

Step3: Substitute values into formula

Substitute $x_1=-6$, $y_1 = 6$ and $m=\frac{1}{4}$ into $y - y_1=m(x - x_1)$. We get $y - 6=\frac{1}{4}(x+6)$.

Answer:

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