Question

Which inequality is correctly represented by this graph

A) 3x-y>3
B) x-3y>=2
C) 3x-y<=3
D)x-3y>2

Answer 1

You should first solve each equation for y.

Eliminate answer choices with wrong slopes or y intercepts.

Then, because it is a dotted line, the answer will only be < or >.

And because the area is shaded to the right, it would mean that x > y.

So the answer is A) 3x - y > 3

Answer 2

The correct option is A.

Explanation:

If a line passing through two points then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

From the given graph it is clear that the related line passing through the points (0,-3) and (1,0). So, the equation of related line is

`y-(-3)=(0-(-3))/(1-0)(x-0)`

`y+3=3x`

The (0,0) is not in the solution set. So check the equation be (0,0).

`0+3=3(0)`

`3=0`

This condition is false if the sign of inequality is < or ≤. Since the related line is a solid line, therefore the sign of inequality must be <.

The required inequality is

`y+3<3x`

`3<3x-y`

It is also written as

`3x-y>3`

Therefore the correct option is A.