Answer:
The correct answer option is C. y<= -4x + 25.
Step-by-step explanation:
Firstly, we will find out the equation of the line with the help of using two points (0, 25) and (-6, 49).
The slope (m) = [tex]\frac{49-25}{-6-0} =-4[/tex].
We know the standard form of the equation is [tex]y=mx+c[/tex] so the y-intercept (c) can be found by putting in the values of the slope and the coordinates of a point.
[tex]25=-4(0)+c\\\\c=25[/tex]
Therefore, the equation of the line is y = -4x + 25.
Now since the inequality is dealing with the value of y and we know that the values of y go vertically (up and down). So if we look at the graph, the shaded area includes the smaller values of y and the line is a solid one.
Therefore, the inequality will be y<= -4x + 25.
If you don't understand it this way, you can pick up a point and test the inequality.
Taking the easiest point (0, 0) to check.
0 <= -4 (0) + 25
0 <= 25 --- True
