What is the Graph of y = c?

S3-SA5-0099

Grade Level:

Class 9

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The graph of y = c is a straight line that runs horizontally across the coordinate plane. Here, 'c' is any constant number, meaning its value never changes. This line shows all the points where the y-coordinate is always equal to 'c', no matter what the x-coordinate is.

Simple Example

Quick Example

Imagine the price of a cup of chai at your local stall is always Rs. 10, no matter how many cups you buy. If 'y' is the price and 'c' is 10, then y = 10. On a graph, this would be a flat line at the '10' mark on the price (y-axis) scale, showing the price stays constant.

Worked Example

Step-by-Step

Let's plot the graph of y = 3.

1. First, understand that 'c' here is 3. This means the y-coordinate for every point on this line will always be 3.

2. Pick some x-values. For example, let's take x = -2, x = 0, and x = 4.

3. For x = -2, y is still 3. So, the point is (-2, 3).

4. For x = 0, y is still 3. So, the point is (0, 3).

5. For x = 4, y is still 3. So, the point is (4, 3).

6. Now, plot these points (-2, 3), (0, 3), and (4, 3) on a graph paper.

7. Connect these points. You will see a straight horizontal line passing through y = 3 on the y-axis.

Answer: The graph of y = 3 is a horizontal line passing through the point (0, 3) on the y-axis.

Why It Matters

Understanding constant functions like y=c is crucial in many fields. In Data Science, it helps analyze data where a value remains steady. In Physics, it could represent constant velocity. Engineers use it to model systems with fixed parameters, helping them design everything from bridges to circuits.

Common Mistakes

MISTAKE: Drawing a vertical line instead of a horizontal line. | CORRECTION: Remember, y = c means the y-value is constant, so the line is parallel to the x-axis (horizontal). A vertical line is for x = c.

MISTAKE: Thinking 'c' must be positive. | CORRECTION: 'c' can be any real number – positive, negative, or zero. If y = -2, the line is horizontal below the x-axis. If y = 0, the line is the x-axis itself.

MISTAKE: Confusing the graph of y = c with y = mx + c. | CORRECTION: y = c is a special case where the slope 'm' is 0. It's a simple horizontal line, not a line that slopes up or down.

Practice Questions

Try It Yourself

QUESTION: Describe the graph of y = -5. | ANSWER: It is a horizontal line passing through y = -5 on the y-axis.

QUESTION: Which axis is the graph of y = 0? | ANSWER: The graph of y = 0 is the x-axis itself.

QUESTION: If a city's average daily temperature remained 25 degrees Celsius for a week, how would you represent this on a graph where the y-axis is temperature and the x-axis is days? | ANSWER: It would be a horizontal line at y = 25.

MCQ

Quick Quiz

Which of the following statements is true about the graph of y = 7?

It is a vertical line.

It passes through the origin (0,0).

It is a horizontal line intersecting the y-axis at (0,7).

Its slope is undefined.

The Correct Answer Is:

The graph of y = c is always a horizontal line. Since c is 7, it will cross the y-axis at the point where y is 7, which is (0,7). Options A and D describe vertical lines or lines with undefined slopes. Option B is incorrect as it does not pass through (0,0) unless c=0.

Real World Connection

In the Real World

Imagine a mobile data plan where you get unlimited data for a fixed monthly charge, say Rs. 300. If 'y' is the monthly cost and 'x' is the data used, the graph of y = 300 would be a horizontal line, showing the cost is constant regardless of data consumption. This is a common pricing model used by telecom companies in India.

Key Vocabulary

Key Terms

CONSTANT: A value that does not change. | COORDINATE PLANE: A 2D surface formed by two perpendicular number lines (x-axis and y-axis). | HORIZONTAL LINE: A straight line parallel to the x-axis. | Y-INTERCEPT: The point where a line crosses the y-axis.

What's Next

What to Learn Next

Now that you understand horizontal lines, you're ready to explore the graph of x = c, which are vertical lines. After that, you can combine this knowledge to understand more complex linear equations like y = mx + c, which have different slopes and intercepts.