Answer:
[tex]\displaystyle y<-\frac{1}{5}x+1[/tex]
Step-by-step explanation:
Graph of an inequality
The graph represented in the image is a line and we have two clear points through which the line passes.
Those points are (0,1) and (5,0).
The equation of a line can have the slope-intercept form:
y=mx+b
Substituting the point (0,1):
1=0+b
b=1
Substituting the point (5,0):
0=m(5)+1
Solving for m:
[tex]\displaystyle m=-\frac{1}{5}[/tex]
The equation of the line is:
[tex]\displaystyle y=-\frac{1}{5}x+1[/tex]
The origin belongs to the solution if we substitute (0,0) the inequality should stand:
0<1
Or:
0≤1
Since the line is dashed, the boundary line is not part of the solution
Thus the inequality is:
[tex]\boxed{\displaystyle y<-\frac{1}{5}x+1}[/tex]
Option D.
