Question

Which of the following inequalities is best represented by this graph?

x - 2y > 3

x - 2y < 3

2x - y > 3

2x - y < 3

Answer 1

Based on the graph we see that the slope is 1/2

By simplifying each of these expressions, that leaves on options 1 and 2 that fit this.

Since the shaded area is going downward, the choice including less than is what's pictured.

Choice One is the correct answer

Answer 2

Answer: x-2y > 3

Explanation:

By the given diagram,

The related line of the inequality is passes through the point (0,-1.5) and (3,0)

Thus, the equation of the related line,

`y-(-1.5)=(0-(-1.5))/((3-0)) (x-0)`

`y+1.5=((0+1.5))/(3)x`

`y+1.5=(1.5)/(3)x`

`y+(15)/(10)=(15)/(30)x`

`y+(3)/(2)=(1)/(2)x`

`(2y+3)/(2)=(1)/(2)x`

`2y+3=x\implies 2y+3-x=0\implies -x+2y=-3\implies x-2y=3`

Thus, the related line of the given inequality is x-2y=3

Hence, the possible inequalities are,

x-2y ≥ 3, x-2y ≤ 3, x-2y > 3 or x-2y < 3

By the given diagram,

The inequality does not contains the origin,

Thus, the possible inequalities are x-2y ≥ 3 or x-2y > 3.

Again,

The doted line shows that the inequality does not contain the equal sign.

Hence, the inequality is,

x-2y > 3

⇒ First option is correct.