Consider the graph of the linear function h(x) = -6 + 2/3 x. Which quadrant will the graph not go through and why.

Question

asked Feb 18, 2019 65.4k views

2 Answers

Resa · Answer 1 · 2019-02-19T02:45:28+0000

There are four quadrants.

I. x>0, y>0

II. x<0, y>0

III. x<0, y<0

IV. x>0, y<0

note that for any x<0, h(x) < 0 (that corresponds to III)

Why?
$(2/3)x <0\\\therefore (2/3)x - 6 < 0$

So, the graph not go through II.

Note that, if x = 3, h(3) = -4 < 0, (that corresponds to IV), and if x = 12, h(12) = 2> 0, that corresponds to I.