Answer:
y ≥ x + 9 and 15x + 4y + 40 > 0
Step-by-step explanation:
The firm line passes through the x-intercept (-9,0) and the y-intercept (0,9) so, the equation of the firm line is
[tex]\frac{x}{- 9} + \frac{y}{9} = 1[/tex]
⇒ -x + y = 9
⇒ y = x + 9
Now, the origin is not in the solution zone of the firm line inequality.
So, the inequality will be y ≥ x + 9 ........ (1)
Again, the dotted line passes through the points (-4,5) and (0,-10)
Therefore, the equation of the dotted line will be
[tex]\frac{y + 10}{- 10 - 5} = \frac{x - 0}{0 + 4}[/tex]
⇒ 4y + 40 = - 15x
⇒ 15x + 4y + 40 = 0
Now, the dotted line inequality includes origin (0,0) in the solution zone.
So, the dotted line inequality will be 15x + 4y + 40 > 0 ......... (2)
Therefore, the system of inequalities for the graph will be from (1) and (2),
y ≥ x + 9 and 15x + 4y + 40 > 0 (Answer)
