The equation of the line in slope-i9ntercept form is
[tex]y=mx+b[/tex]where m is the slope and b is the intercept
First we need to calculate the slope with the next formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]we need two points of the line
(0,-2)=(x1,y1)
(-4,0)=(x2,y2)
we substitute the points in the formula
[tex]m=\frac{0+2}{-4+0}=\frac{2}{-4}=-\frac{1}{2}[/tex]then we need to know the values of the y-intercept that is the value of the coordinate y when x is equal to 0
in our case is -2
Therefore the equation of the line is
[tex]y=-\frac{1}{2}x-2[/tex]as we can see the correct choice is a