Question

Which of the following systems of inequalities would produce the region

indicated on the graph below?

A. y ≥ x + 1 ; y ≥ 10 ; x ≥ 0
B. y > x + 1 ; y ≤ 10 ; x ≥ 0
C. y < x + 1 ; y ≤ 10 ; x ≥ 0
D. y ≥ x + 1 ; y < 10 ; x ≥ 0

Answer 1

y > x + 1 ; y ≤ 10 ; x ≥ 0

Explanation:

First, we need to get the equation of the straight line. The equation of the straight line is expressed as y = mx+c

m is the slope

c is the y-intercept

Using the coordinate points (0, 1) and (1,2)

m = (2-1)/(1-0)

m = 1/1 = 1

y-intercept c = 1 (the point where the line cuts the y-axis)

Substitute;

Since y = mx+c, then y = 1x + 1

y = x+1

Since the line is a broken line and shaded above, then y > x+1

Also, the point shaded on the graph indicates y ≤ 10 ; x ≥ 0