232k views
5 votes
What system of inequalities is represented by the graph?

A. y < or equal to 5x -1 and -3x + y > or equal to 4
B. y < or equal to 5x -1 and 3x + y > or equal to 4
C. y < or equal to 5x + 1 and 3x + y > or equal to 4
D. y < or equal to 5x - 1 and 3x + y > or equal to -4

What system of inequalities is represented by the graph? A. y < or equal to 5x-example-1
User WojonsTech
by
8.1k points

1 Answer

7 votes
As shown in the figure, we have two straight line. One of them has a negative slope and the other has a positive one. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form by:


y=mx+b

being m the slope of the line and b the y-intercept of it.

On the other hand, if x = 0 then y = b.

First of all we will order the equations above without inequalities like this:

A.

y = 5x-1,
y = 3x+4
B.
y = 5x-1,
y = -3x+4
C.
y = 5x+1,
y = -3x+4
D.
y = 5x-1,
y = -3x-4

As shown in the figure b = -1 for one straight and b = 4 for the second one. This values take place when x = 0. So, we discard C and D, because if x = 0, then:

For C, b = 1 and b = 4
For D, b = -1 and b = -4

Let's analyze A and B. So:

For A, m = 5 and m = 3
For B, m = 5 and m = -3

Therefore, we discard A because of the statement above.

Finally the answer is B. So, the inequalities are:

(1)
y\ \textless \ 5x-1
(2)
3x+y \geq 4

Let's prove this answer. We will take the point (2, 0) that is in the region in gray. So, substituting this point in the inequalities, we have:

(1)
0\ \textless \ 9
(2)
6 \geq 4

In fact, this is true.


User Fadedbee
by
8.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories