Question

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

Answer 1

Answer: x-2y > 3

Step-by-step 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,

$y-(-1.5)=\frac{0-(-1.5)}{(3-0)} (x-0)$

$y+1.5=\frac{(0+1.5)}{3}x$

$y+1.5=\frac{1.5}{3}x$

$y+\frac{15}{10}=\frac{15}{30}x$

$y+\frac{3}{2}=\frac{1}{2}x$

$\frac{2y+3}{2}=\frac{1}{2}x$

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

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.

Answer 2

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