Find the X-Axis Intersection Point of a Horizontal Line Graph

Horizontal Lines with No X-Intercept

At what point does the graph intersect the x axis?



111222333444555666777–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333000xyII

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 At which point does the graph intersect the X axis?
00:03 Looking at the X axis, we can see that the graph is parallel to it
00:07 Therefore it doesn't intersect the X axis at all
00:10 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

At what point does the graph intersect the x axis?



111222333444555666777–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333000xyII

2

Step-by-step solution

Note that the line intersects only the Y-axis. In other words, it does not go through the X-axis at all.

Therefore, the answer is (d).

3

Final Answer

It does not intersect the x axis.

Key Points to Remember

Essential concepts to master this topic
  • Horizontal Line Rule: y equals constant means line is parallel to x-axis
  • X-Intercept Check: Set y = 0 and solve; if no solution exists, no x-intercept
  • Visual Verification: Line stays at y = 2, never touches x-axis ✓

Common Mistakes

Avoid these frequent errors
  • Assuming all lines must intersect both axes
    Don't automatically assume every line crosses the x-axis = wrong conclusion! Horizontal lines at y ≠ 0 never touch the x-axis since they maintain constant height. Always check if the line actually passes through y = 0.

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

xy

FAQ

Everything you need to know about this question

How can a line not intersect the x-axis?

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A horizontal line at y = 2 (like in this graph) runs parallel to the x-axis and stays at a constant height. Since it never drops down to y = 0, it never touches the x-axis!

What's the difference between x-intercept and y-intercept?

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An x-intercept is where the line crosses the x-axis (y = 0), written as (x, 0). A y-intercept is where it crosses the y-axis (x = 0), written as (0, y).

Do all horizontal lines avoid the x-axis?

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No! The horizontal line y=0 y = 0 is the x-axis itself, so it intersects at every point. Only horizontal lines where y0 y ≠ 0 don't intersect the x-axis.

How do I find where any line intersects the x-axis?

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Set y = 0 in the line's equation and solve for x. If you get a specific x-value, that's your x-intercept. If the equation becomes impossible (like 2 = 0), there's no x-intercept.

What does 'parallel to the x-axis' mean?

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Parallel means the lines never meet - they maintain the same distance apart forever. A horizontal line stays the same distance above (or below) the x-axis at all points.

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