What is a Graph of y = c?

S3-SA5-0260

Grade Level:

Class 9

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

Definition

What is it?

A graph of y = c represents a straight horizontal line on a coordinate plane. Here, 'c' is any constant number, meaning the y-value always stays the same, no matter what the x-value is.

Simple Example

Quick Example

Imagine the price of a small packet of biscuits is fixed at Rs 10. If you plot the price (y-axis) against the number of packets bought (x-axis), the price will always be Rs 10, no matter how many packets you buy. This creates a straight horizontal line at y = 10.

Worked Example

Step-by-Step

Let's draw the graph of y = 3.

Step 1: Understand the equation. y = 3 means that for every point on the line, the y-coordinate will always be 3.

Step 2: Choose a few x-values. Since y is always 3, x can be any number. Let's pick x = -2, 0, 1, 3.

Step 3: Find the corresponding y-values. For x = -2, y = 3. For x = 0, y = 3. For x = 1, y = 3. For x = 3, y = 3.

Step 4: List the coordinates. We have points (-2, 3), (0, 3), (1, 3), (3, 3).

Step 5: Plot these points on a coordinate plane. Mark each point carefully.

Step 6: Draw a straight line passing through all these points. You will see it's a horizontal line, 3 units above the x-axis.

Answer: The graph of y = 3 is a horizontal line parallel to the x-axis, passing through all points where the y-coordinate is 3.

Why It Matters

Understanding these basic graphs is crucial for many fields! In Data Science, you might see constant values representing fixed costs or limits. In Physics, it could show a body moving at a constant speed. This foundation helps future engineers and scientists analyze complex data and build models.

Common Mistakes

MISTAKE: Students sometimes draw y = c as a vertical line. | CORRECTION: Remember 'y' refers to vertical position. If y is constant, the line must be horizontal.

MISTAKE: Students confuse y = c with x = c. | CORRECTION: y = c is a horizontal line, while x = c (where x is constant) is a vertical line.

MISTAKE: Students think y = c means it only exists at x = 0. | CORRECTION: y = c means y is 'c' for ALL possible x-values, extending infinitely in both positive and negative x directions.

Practice Questions

Try It Yourself

QUESTION: Which axis is the graph of y = 5 parallel to? | ANSWER: x-axis

QUESTION: Plot the points (0, -2), (3, -2), (-4, -2) and connect them. What is the equation of the line you drew? | ANSWER: y = -2

QUESTION: A small tiffin service charges Rs 80 for every meal, regardless of how many meals you order in a month. If 'y' is the cost and 'x' is the number of meals, write the equation for the total cost and describe its graph. | ANSWER: Equation: y = 80. The graph is a horizontal line 80 units above the x-axis, parallel to the x-axis.

MCQ

Quick Quiz

What kind of line does the equation y = -7 represent on a coordinate plane?

A vertical line

A horizontal line

A diagonal line

A curved line

The Correct Answer Is:

When y is equal to a constant number, the y-coordinate never changes, resulting in a horizontal line. A vertical line would be x = constant.

Real World Connection

In the Real World

Imagine a thermometer in Delhi showing a constant temperature of 35 degrees Celsius for an hour. If you graph temperature (y-axis) against time (x-axis), you'd get a horizontal line at y=35. This helps meteorologists visualize stable conditions.

Key Vocabulary

Key Terms

CONSTANT: A value that does not change. | COORDINATE PLANE: A 2D surface where points are located using x and y coordinates. | HORIZONTAL LINE: A straight line that goes from left to right, parallel to the x-axis. | Y-AXIS: The vertical number line on a coordinate plane.

What's Next

What to Learn Next

Great job understanding y = c! Next, explore the graph of x = c. It's a similar concept but creates a different type of line, and understanding both will give you a solid foundation for more complex linear equations!