Question

Use the clues given to make a graph. Then write an equation that fits the graph of the line.
1. Draw a line that is only in quadrants​ II, III, and IV. The​ y-intercept is at least minus6 and no greater than minus3.
2. Draw a line that is only in quadrants I and II. The​ y-intercept is 5.
3. Draw a line that is only in quadrants I and III. The​ y-intercept is 0.
4. Draw a line that is only in quadrants III and IV. The​ y-intercept is minus3.
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Part 1
1. Which of the following shows a line that is only in quadrants​ II, III, and IV and whose​ y-intercept is at least minus6 and no greater than minus​3?
A.
-10
10
-10
10
x
y



x y graph
B.
-10
10
-10
10
x
y



x y graph
C.
-10
10
-10
10
x
y



x y graph
D.
-10
10
-10
10
x
y



x y graph
Which of the following shows a line that is only in quadrants II, III, and IV and whose y-intercept is at least 6 and no greater than 3?
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Answer 1

I can’t see the four pictured graphs, so I’ll (A) give equations that satisfy each clue and explain how to recognize the correct graph, and (B) tell you how to pick the correct multiple‑choice picture.

Equations and reasoning

1) "Only in quadrants II, III, and IV. y‑intercept between −6 and −3."
- Choose any negative slope and a y‑intercept b with −6 ≤ b ≤ −3. Example: y = −x − 4.
- Why: negative slope (m < 0) gives positive y for some x < 0 (quadrant II) and negative y for x > 0 (quadrant IV); b is negative so the line crosses the y‑axis below 0 and never enters quadrant I.

2) "Only in quadrants I and II. y‑intercept 5."
- Must be horizontal with positive y‑intercept so y never becomes ≤ 0. Example: y = 5.
- Why: any nonzero slope would make y eventually negative for large |x|, so only a horizontal line y = 5 stays entirely in the top half‑plane (quadrants I and II).

3) "Only in quadrants I and III. y‑intercept 0."
- Any line through the origin with positive slope works. Example: y = 2x.
- Why: y = mx with m > 0 makes y have the same sign as x, so points lie only where x and y have the same sign (I and III).

4) "Only in quadrants III and IV. y‑intercept −3."
- Must be the horizontal line y = −3.
- Why: to keep y strictly negative for all x you need a horizontal line with b < 0; any nonzero slope would force y positive for some x.

How to choose the correct multiple‑choice picture for Part 1
- Look for the line that (a) crosses the y‑axis at a point between −6 and −3, and (b) slopes downward (negative slope), and (c) does not pass into quadrant I. If you see a downward line whose intersection with the y‑axis is at a negative value between −6 and −3, that is the correct picture.
- If you can send or describe the four images (where each line crosses the axes, or the slope direction), I’ll pick A–D for you.

If you want, I can also sketch these on a coordinate grid (ASCII description) or give alternate example equations.