Question

Can someone please help mee.

Answer 1

`\displaystyle y<-(1)/(5)x+1`

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:

`\displaystyle m=-(1)/(5)`

The equation of the line is:

`\displaystyle y=-(1)/(5)x+1`

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:

`\boxed{\displaystyle y<-(1)/(5)x+1}`

Option D.