Question

which inequality does the given graph represents? A
`y \ \textgreater \ 4x + 3`B
`y \ \textgreater \ - 4x + 3`C
`y \ \textgreater \ (1)/(4) x + 3`D
`y \ \textless \ - 4x + 3`

Answer 1

The shaded area represents the inequality

The equations are in the form of the equation y=mx+c where m is the slope of the graph and c is the y intercept except for the inequality sign in place of '='.

The given graph has a negative slope

So, here options (B) or (c) has negative slopes if we compare the inequallity equations with y=mx+c

Now , we take a point (2,0) which comes in the shaded part.

For option(B),y>-4x+3

Substitute (x,y)=(2,0) in this equation

We write it as 0>-4X2+3

0>-8+3

0>-5 is true

Now consider option(D), y<-4x+3.

Substitute(x,y)= (2,0) in y<-4x+3.

Then, 0<-4X2+3

0<-8+3

0<-5 is incorrect.

So, the answer is option(B)