Which inequality is represented by the graph? A) y≥−12x+2.5 B) y>−2x+2.5 C) y≥−2x+2.5 D) y≤−2x+2.5

Question

asked Jun 19, 2020 173k views

2 Answers

Emjee · Answer 1 · 2020-06-23T20:24:04+0000

Answer:

Option C.

Explanation:

If a line passes through two points
(x_1,y_1) and
(x_2,y_2) , 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 passes thorough the points (0,2.5) and (2,-1.5).

The equation of related line is

y-2.5=(-1.5-2.5)/(2-0)(x-0)

y-2.5=(-4)/(2)(x)

y-2.5=-2x

Add 2.5 on both sides.

y-2.5+2.5=-2x+2.5

y=-2x+2.5

Th sign of inequality is either ≤ or ≥ because the related line is a solid line. It means the points on the line are included in the solution set.

Let the required inequality is

$y\geq -2x+2.5$

(1,1) is included in the shaded region. So, the above inequality is true for (1,1).

$1\geq -2(1)+2.5$

$1\geq 0.5$

The assumed inequality is true for (1,1). So, the required inequality isn
$y\geq -2x+2.5$ .

Therefore, the correct option is C.