Question

write the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Identify two points on the line

Let's take the points $(- 6,-2)$ and $(6,1)$.

Step2: Calculate the slope $m$

The slope - formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the values: $m=\frac{1-(-2)}{6 - (-6)}=\frac{1 + 2}{6+6}=\frac{3}{12}=\frac{1}{4}$.

Step3: Use the slope - intercept form $y=mx + b$ and a point to find $b$

Using the point $(6,1)$ and $m=\frac{1}{4}$, we substitute into $y=mx + b$: $1=\frac{1}{4}\times6 + b$. Then $1=\frac{6}{4}+b$, and $b=1-\frac{6}{4}=\frac{4 - 6}{4}=-\frac{1}{2}$.

Step4: Write the equation of the line

The equation of the line in slope - intercept form is $y=\frac{1}{4}x-\frac{1}{2}$.

Answer:

$y=\frac{1}{4}x-\frac{1}{2}$