Question

In which quadrants do solutions for the inequality y is less than or equal to two sevenths times x plus 1 exist? i, iii, and iv i, ii, and iii i and iv all four quadrants

Answer 1

The solutions will lie  in all the four quadrants.

y≤2/7x+1

We have the following inequality:

y=2/7x+1

If x=0

y=2/7(0) +1

y=1

If y=0

x=-3.5

So the line passes through the points:

(0,1) and (-3.5,0)

To find the shaded region, let us take a point, namely, the origin and test it in the inequality:

y≤ 2/7x +1

0≤ 2/7(0) +1

0≤ 1 which is true

Since this is true, then the shaded region includes this point. This is shown below and as you can see the solutions exist in all four quadrants.

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