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 $(0, - 2)$, so $b=-2$.

Step2: Calculate the slope

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

Step3: Write the equation in slope - intercept form

The slope - intercept form of a line is $y=mx + b$. Substituting $m =-\frac{1}{2}$ and $b=-2$ into the formula, we get $y=-\frac{1}{2}x-2$.

Answer:

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