Question

find the equation of this line. y = - \frac{?}{?}x +

Explanation:

Step1: Find the slope

The line passes through (-4,0) and (0, - 2). The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-4,y_1 = 0,x_2=0,y_2=-2$. So $m=\frac{-2 - 0}{0-(-4)}=-\frac{2}{4}=-\frac{1}{2}$.

Step2: Find the y - intercept

The y - intercept $b$ is the value of $y$ when $x = 0$. From the graph, when $x = 0$, $y=-2$. The equation of a line is $y=mx + b$. Substituting $m =-\frac{1}{2}$ and $b=-2$ into the equation, we get $y=-\frac{1}{2}x-2$.

Answer:

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