Answer:
[tex]\displaystyle 4x + 3y < 15\:or\:y < -1\frac{1}{3}x + 5[/tex]
Step-by-step explanation:
First, find the rate of change [slope]. From [tex]\displaystyle [3, 1],[/tex]travel three units west over four units north, where you will arrive at the y-intercept of [tex]\displaystyle [0, 5].[/tex]Doing this will lead you to knowing that the rate of change is [tex]\displaystyle -1\frac{1}{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 + 5}{-3 \pm 0} \hookrightarrow \frac{4}{-3} \\ \\ \boxed{-1\frac{1}{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 < -1\frac{1}{3}[0] + 5; \boxed{0 < 5} \\ 0 > -1\frac{1}{3}[0] + 5; \boxed{0 \ngtr 5}[/tex]
Therefore, sinse this graph has a dashed line AND is 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 < -1\frac{1}{3}x + 5.[/tex]
I am joyous to assist you at any time.
