Coordinate Geometry: Analyzing Three Intersecting Lines in the X-Y Plane

Line Behavior with Slope Analysis

Choose the correct answer

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Choose the correct answer

xy

2

Step-by-step solution

The blue line is a straight line, therefore it remains constant.

Let's note that the red line is rising because it starts in the negative part (negative values) and rises to the positive part (positive values).

Therefore, the correct answer is D.

3

Final Answer

Answers B and C are correct

Key Points to Remember

Essential concepts to master this topic
  • Slope Analysis: Positive slope means increasing, zero slope means constant
  • Visual Method: Red line rises left to right with positive slope
  • Verification: Check direction from left to right on coordinate plane āœ“

Common Mistakes

Avoid these frequent errors
  • Confusing horizontal with increasing lines
    Don't assume all diagonal lines are increasing = wrong slope interpretation! A line going down from left to right has negative slope and is decreasing. Always check if y-values increase or decrease as x increases from left to right.

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

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FAQ

Everything you need to know about this question

How do I tell if a line is increasing or decreasing?

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Look at the line from left to right. If it goes up, it's increasing (positive slope). If it goes down, it's decreasing (negative slope). If it stays level, it's constant (zero slope).

What makes a line constant?

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A horizontal line is constant because it has the same y-value everywhere. No matter what x-value you pick, y never changes - that's why the slope is zero!

Can a line be both increasing and decreasing?

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No! A straight line has only one slope throughout its entire length. It's either increasing, decreasing, or constant - never a combination.

What if the line looks steep - does that matter?

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Steepness tells you how fast the line increases or decreases, but doesn't change whether it's increasing or decreasing. A steep line still follows the left-to-right rule!

Why does the red line count as increasing?

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Even though the red line starts below the x-axis, it's still rising from left to right. The key is the direction of change, not where it starts or ends.

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