November 11, 2022

Y-Intercept - Definition, Examples

As a student, you are always looking to keep up in class to prevent getting swamped by topics. As guardians, you are constantly researching how to motivate your kids to prosper in academics and after that.

It’s particularly important to keep up in mathematics because the theories constantly founded on themselves. If you don’t understand a specific lesson, it may haunt you for months to come. Comprehending y-intercepts is an ideal example of topics that you will revisit in mathematics over and over again

Let’s look at the basics about y-intercept and take a look at some tips and tricks for solving it. Whether you're a math wizard or just starting, this introduction will enable you with all the things you need to learn and instruments you require to tackle linear equations. Let's get into it!

What Is the Y-intercept?

To fully comprehend the y-intercept, let's imagine a coordinate plane.

In a coordinate plane, two straight lines intersect at a junction known as the origin. This section is where the x-axis and y-axis meet. This means that the y value is 0, and the x value is 0. The coordinates are stated like this: (0,0).

The x-axis is the horizontal line passing across, and the y-axis is the vertical line traveling up and down. Every axis is counted so that we can specific points along the axis. The numbers on the x-axis grow as we shift to the right of the origin, and the numbers on the y-axis grow as we move up from the origin.

Now that we have revised the coordinate plane, we can determine the y-intercept.

Meaning of the Y-Intercept

The y-intercept can be considered as the starting point in a linear equation. It is the y-coordinate at which the coordinates of that equation crosses the y-axis. Simply said, it represents the number that y takes while x equals zero. Next, we will show you a real-life example.

Example of the Y-Intercept

Let's suppose you are driving on a straight road with a single lane runnin in both direction. If you begin at point 0, location you are sitting in your car right now, then your y-intercept will be similar to 0 – considering you haven't moved yet!

As you initiate you are going the road and picking up speed, your y-intercept will increase before it reaches some greater value once you reach at a designated location or halt to induce a turn. Consequently, once the y-intercept may not look particularly applicable at first glance, it can provide knowledge into how things transform over a period of time and space as we shift through our world.

So,— if you're ever puzzled trying to understand this theory, bear in mind that almost everything starts somewhere—even your journey through that long stretch of road!

How to Find the y-intercept of a Line

Let's comprehend regarding how we can discover this number. To support you with the method, we will outline a some steps to do so. Then, we will give you some examples to demonstrate the process.

Steps to Discover the y-intercept

The steps to locate a line that goes through the y-axis are as follows:

1. Find the equation of the line in slope-intercept form (We will dive into details on this afterwards in this article), which should appear similar this: y = mx + b

2. Replace 0 in place of x

3. Figure out y

Now once we have gone over the steps, let's check out how this process would work with an example equation.

Example 1

Locate the y-intercept of the line described by the formula: y = 2x + 3

In this example, we could replace in 0 for x and figure out y to locate that the y-intercept is the value 3. Thus, we can say that the line crosses the y-axis at the point (0,3).

Example 2

As additional example, let's consider the equation y = -5x + 2. In this case, if we replace in 0 for x one more time and figure out y, we find that the y-intercept is equal to 2. Therefore, the line crosses the y-axis at the coordinate (0,2).

What Is the Slope-Intercept Form?

The slope-intercept form is a procedure of depicting linear equations. It is the commonest kind used to represent a straight line in scientific and mathematical uses.

The slope-intercept equation of a line is y = mx + b. In this function, m is the slope of the line, and b is the y-intercept.

As we checked in the previous portion, the y-intercept is the coordinate where the line goes through the y-axis. The slope‌ is a scale of how steep the line is. It is the unit of change in y regarding x, or how much y moves for every unit that x shifts.

Since we have reviewed the slope-intercept form, let's observe how we can employ it to locate the y-intercept of a line or a graph.


Find the y-intercept of the line state by the equation: y = -2x + 5

In this equation, we can observe that m = -2 and b = 5. Therefore, the y-intercept is equal to 5. Therefore, we can say that the line goes through the y-axis at the point (0,5).

We can take it a step further to illustrate the slope of the line. In accordance with the equation, we know the inclination is -2. Plug 1 for x and figure out:

y = (-2*1) + 5

y = 3

The solution tells us that the next point on the line is (1,3). When x changed by 1 unit, y changed by -2 units.

Grade Potential Can Help You with the y-intercept

You will review the XY axis over and over again during your science and math studies. Theories will get more difficult as you advance from working on a linear equation to a quadratic function.

The time to master your understanding of y-intercepts is now before you straggle. Grade Potential provides expert teacher that will guide you practice finding the y-intercept. Their customized explanations and work out problems will make a good distinction in the results of your examination scores.

Anytime you believe you’re stuck or lost, Grade Potential is here to guide!