Answer:
option D: [tex]5x-6y \geq -30[/tex]
Step-by-step explanation:
To write the inequality for the given graph we need to pick two points from the graph to frame the equation of the line.
Two point on the graph are (0,5) and (-6,0)
Now frame the equation y=mx+b, where m is the slope and b is the y intercept
Here y intercept is the point where the graph crosses y axxis and it is equal to 5. [tex]b=5[/tex]
slope m = [tex]\frac{y2-y1}{x2-x1}=\frac{0-5}{-6-0}=\frac{5}{6}[/tex]
So equation becomes [tex]y= \frac{5}{6} x+5[/tex]
Multiply the whole equaiton by 6
[tex]6y=5x+30[/tex]
Subtract 5x on both sides
[tex]-5x+6y= 30[/tex] Multiply whole equation by -1
[tex]5x-6y= -30[/tex]
Now we look at the shaded part and confirm the inequality
The shaded part contains (0,0)
So we plug in 0 for x and 0 for y
[tex]5(0)-6(0)= -30[/tex]
[tex]0 \geq -30[/tex]True
So inequality becomes [tex]5x-6y \geq -30[/tex]
