question\nwrite the equation of the line in fully simplified slope - intercept form.

Explanation:

Step1: Identify two points on the line

Let's take the points $(0, - 6)$ and $(6,-5)$.

Step2: Calculate the slope $m$

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substituting the points: $m=\frac{-5-(-6)}{6 - 0}=\frac{-5 + 6}{6}=\frac{1}{6}$.

Step3: Identify the y - intercept $b$

The y - intercept is the y - value when $x = 0$. From the point $(0,-6)$, $b=-6$.

Step4: Write the equation in slope - intercept form

The slope - intercept form is $y=mx + b$. Substituting $m=\frac{1}{6}$ and $b=-6$, we get $y=\frac{1}{6}x-6$.

Answer:

$y=\frac{1}{6}x - 6$