Question

Which inequality is represented by the graph?y > -2/3x + 1y < -2/3x + 1y < -3/2x + 1y > -3/2x + 1

Answer 1

For those who don’t want to read all that the answer is c y<-3/2x+1

Answer 2

`y < -(3)/(2)x+1`

Explanation:

Given:

From the graph shown,

The broken line means that the inequality sign will be either < or >.

The shaded region is to the left of the broken line. This means that
`y < f(x)`.

Now, in order to find equation of line, we need slope and y-intercept.

From the graph, the y intercept is at
`(0,1)`. So, y intercept is 1.

Also, if we consider two points
`(0,1)\textrm{ and }(2,-2)` on the line, then slope is given as:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))=(-2-1)/(2-0)=(-3)/(2)=-(3)/(2)`

Therefore, the equation of the line is given as:

`y=mx+b\\y=-(3)/(2)x+1`

But as the shaded region is to the left of the line,

∴
`y<-(3)/(2)x+1` is the correct answer.