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: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the line, say $(0,-2)$ and $(2,-4)$. Then $m=\frac{-4-(-2)}{2 - 0}=\frac{-4 + 2}{2}=\frac{-2}{2}=-1$.

Step2: Find the y - intercept

The y - intercept $b$ is the y - value when $x = 0$. From the graph, when $x = 0$, $y=-2$, so $b=-2$.

Step3: Write the equation

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

Answer:

$y=-x - 2$