What is the Y-intercept?

S6-SA1-0066

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

The Y-intercept is the point where a line crosses the Y-axis on a graph. At this point, the value of 'x' is always zero. It tells us the starting value or initial condition of something being measured.

Simple Example

Quick Example

Imagine you are tracking how much money you save each day. If you start with ₹50 in your piggy bank, and then add more money daily, the ₹50 is your Y-intercept. It's the amount you had at the very beginning (when 'days passed' was zero).

Worked Example

Step-by-Step

Let's find the Y-intercept for the equation y = 2x + 3.

Step 1: Remember that the Y-intercept is where the line crosses the Y-axis. This means the x-coordinate at that point is always 0.

Step 2: Substitute x = 0 into the equation.
y = 2(0) + 3

Step 3: Perform the multiplication.
y = 0 + 3

Step 4: Perform the addition.
y = 3

Step 5: The Y-intercept is the point where x is 0 and y is 3.

Answer: The Y-intercept is (0, 3).

Why It Matters

Understanding the Y-intercept helps scientists and engineers find starting points in experiments or designs. In careers like data analysis or medicine, it helps predict initial outcomes or understand baseline values. It's a fundamental concept for building models in AI/ML and understanding physical phenomena.

Common Mistakes

MISTAKE: Confusing the Y-intercept with the X-intercept. | CORRECTION: The Y-intercept is where x=0, while the X-intercept is where y=0. They are different points on the graph.

MISTAKE: Forgetting to set x=0 when finding the Y-intercept from an equation. | CORRECTION: Always substitute x=0 into the equation to find the corresponding y-value for the Y-intercept.

MISTAKE: Stating only the y-value as the Y-intercept, e.g., 'The Y-intercept is 5'. | CORRECTION: The Y-intercept is a point, so it should be written as an ordered pair (0, y), e.g., (0, 5).

Practice Questions

Try It Yourself

QUESTION: What is the Y-intercept for the equation y = 5x - 7? | ANSWER: (0, -7)

QUESTION: A taxi charges a base fare of ₹30 plus ₹10 per kilometer. Write an equation and find the Y-intercept. | ANSWER: Equation: y = 10x + 30. Y-intercept: (0, 30)

QUESTION: The cost of a mobile data plan is given by C = 150 + 20D, where C is the total cost and D is the number of GB used. What does the Y-intercept represent in this scenario? | ANSWER: The Y-intercept is (0, 150). It represents the fixed monthly charge of ₹150 even if no data (0 GB) is used.

MCQ

Quick Quiz

For the equation y = 4 - 3x, what is the Y-intercept?

(4, 0)

(0, 4)

(-3, 0)

(0, -3)

The Correct Answer Is:

To find the Y-intercept, we set x = 0. Substituting x = 0 into y = 4 - 3x gives y = 4 - 3(0), which simplifies to y = 4. So the Y-intercept is (0, 4).

Real World Connection

In the Real World

When you open a new mobile app, sometimes it gives you a 'welcome bonus' or a 'first-time discount'. If you plot your benefits over time, this initial bonus amount is like the Y-intercept. Similarly, in cricket, if a team starts with some penalty runs before the match, that's their Y-intercept on the score sheet.

Key Vocabulary

Key Terms

Y-AXIS: The vertical line on a graph | X-AXIS: The horizontal line on a graph | COORDINATE: A set of values that show an exact position on a graph | EQUATION: A statement that two mathematical expressions are equal

What's Next

What to Learn Next

Great job understanding the Y-intercept! Next, you should explore the 'X-intercept'. It's the sister concept to the Y-intercept and together they help you fully understand how lines behave on a graph and how to plot them accurately.