Answer:
[tex]\displaystyle 3x - y > 4\:or\:y < 3x - 4[/tex]
Step-by-step explanation:
First, find the rate of change [slope]. From [tex]\displaystyle [1, -1],[/tex]travel three units south over one unit west, where you will arrive at the y-intercept of [tex]\displaystyle [0, -4].[/tex]Doing this will lead you to knowing that the rate of change is [tex]\displaystyle 3.[/tex] Moreover, you could have also done this with the rate of change formula:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \\ \frac{1 - 4}{-1 \pm 0} \hookrightarrow \frac{-3}{-1} \\ \\ \boxed{3 = m}[/tex]
Here you are!
Now we insert this information into the Slope-Intercept formula, but BEFORE doing this, sinse we are dealing with the inequality version of the Slope-Intercept formula, we need to initiate the zero-interval test to determine the inequality symbol of the function. Here is how it is done:
[tex]\displaystyle 0 < 3[0] - 4; \boxed{0 \nless -4} \\ 0 > 3[0] - 4; \boxed{0 > -4}[/tex]
Therefore, sinse this graph has a dashed line AND is not shaded in the area that contains the origin, the less than symbol is suitable for this function, which means the slope-intercept inequality is [tex]\displaystyle y < 3x - 4.[/tex]
I am joyous to assist you at any time.
