Question

A graph is shown below:

solid line joining ordered pair 0, negative 2 and 1, 3 and the region below this line is shaded

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

5x + y ≤ 2
5x + y ≥ 2
5x − y ≤ 2
5x − y ≥ 2

Answer 1

5x-y≥2

Explanation:

Answer 2

1.
The line joins (0, -2) and (1, 3).

thus, the slope of this line is

`(y_1-y_2)/(x_1-x_2)= (-2-3)/(0-1)= (-5)/(-1)=5`

Using point (0, -2) and slope m=5, the equation of the line is:

y-(-2)=5(x-0)
y+2=5x

5x-y=2

2.
Thus the candidate inequalities are

5x-y≥2 and 5x-y≤2

3.
Pick a point P not on the line, for example P(0, -3) which is clearly below the line, which is the shaded part.

check (x,y)=(0,-3) in 5x-y≥2:

5*0-(-3)≥2

3≥2, which is true

Remark: If we had picked a point above the line, for example P(0,2), we would have

5x-y≥2:
5*0-2≥2:
-2≥2, not true, but we would pick again this inequality, since the second point was not on the colored region.


Answer:

5x-y≥2