EXPLANATION
We can write an inequality in slope-intercept form by using the two given points, (x_1,y_1)= (-4,0) and (x_2,y_2)=(4,2), as shown as follows:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]
Replacing terms:
[tex]\text{Slope}=\frac{(2-0)}{(4-(-4))}[/tex]
Subtracting terms:
[tex]\text{Slope}=\frac{2}{8}=\frac{1}{4}[/tex]
Now, we need to find the y-intercept.
As we can see in the dashed line, the y-intercept is at point (x,y)=(0,1).
Hence, the equation of the dashed line is as follows:
y = (1/4)x + 1
But as the solution represents all the points that are below this line, the inequality should be as following:
y < (1/4)x + 1
