Question

Which of the following inequalities matches the graph?

graph of an inequality with a solid line through the points 0, negative 2 and 2, 1 with shading above the line

3x − 2y ≥ 4
3x − 4y ≤ 2
3x − 2y ≤ 4
The correct inequality is not listed.

Answer 1

Answer:

The correct option is 3.

Step-by-step explanation:

It is given a graph of an inequality with a solid line through the points (0, −2) and (2, 1) with shading above the line.

The equation of a solid line is:

$y-y_{1} = \frac{y_{2}- y_{1} }{x_{2}- x_{1} } (x-x_{1})\\ y+2= \frac{1+2}{2-0}(x-0)\\ y+2= \frac{3}{2} x$

The y-intercept of the line is -2 and the shaded region is shading above the line. So, (0,0) must be lies in the shaded region.

Check the related equation by point (0,0).

0+2 =$\frac{3}{2}(0)$

2 = 0

The statement is true if and only if the sign is greater than or equal instead of equal.

The required inequality is

$y+2 \geq \frac{3}{2}x$

Multiply both sides by 2.

$2y + 4 \geq 3x\\4\geq 3x-2y\\3x-2y \leq 4$

Therefore option 3 is correct.

Read to see a similar question about inequalities in the graph:

https://brainly.com/question/23511411?referrer=searchResults

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