Question

write the equation of this line in slope - intercept form. write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify the y - intercept

The line crosses the y - axis at the point $(0, - 6)$. So, $b=-6$.

Step2: Calculate the slope

Choose two points on the line, say $(0, - 6)$ and $(8,-4)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-4-(-6)}{8 - 0}=\frac{-4 + 6}{8}=\frac{2}{8}=\frac{1}{4}$.

Step3: Write the equation in slope - intercept form

The slope - intercept form of a line is $y=mx + b$. Substituting $m = \frac{1}{4}$ and $b=-6$, we get $y=\frac{1}{4}x-6$.

Answer:

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