Question

Choose the linear inequality that describes the graph. The gray area represents the shaded region.

Answer 1

The inequality expression that describes the graph is 2x + 3y ≥ 5

Write an inequality to represent the graph.

From the question, we have the following parameters that can be used in our computation:

The graph

A linear equation is represented as

y = mx + c

Where

c = y when x = 0 i.e. the y-intercept

From the graph, we have the following points

(1, 1) and (-2, 3)

This means that the slope is

m = (3 - 1)/(-2 - 1)

Evaluate

m = -2/3

Using the above as a guide, we have the following:

y = -2/3x + c

Using the point (1, 1), we have the following

-2/3 * 1 + c = 1

c = 1 + 2/3

Evaluate

c = 5/3

So, we have

y = -2/3x + 5/3

Considering the shaded region and the line type, we have

y ≥ -2/3x + 5/3

Multiply through by 3

3y ≥ -2x + 5

Add 2x to both sides of the inequality expression

2x + 3y ≥ 5

Hence, the inequality is 2x + 3y ≥ 5

Answer 2

2x + 3y ≥ 5

Explanation:

See the graph attached.

The bold straight line passes through the points (1,1) and (4,-1).

Therefore, the equation of the straight line will be

`(y + 1)/(- 1 - 1) = (x - 4)/(4 - 1)`

⇒ 3(y + 1) = - 2(x - 4)

⇒ 3y + 3 = - 2x + 8

⇒ 2x + 3y = 5 ............. (1)

Now, the shaded region i.e. the solution to the inequality does not include the origin(0,0).

So, putting x = 0 and y = 0 in the equation (1) we get, 0 < 5

Therefore, the inequality equation is 2x + 3y ≥ 5 (Answer)