November 11, 2022

Y-Intercept - Definition, Examples

As a student, you are constantly working to keep up in class to avoid getting engulfed by subjects. As parents, you are always searching for ways how to motivate your kids to prosper in academics and beyond.

It’s specifically critical to keep up in math due to the fact that the ideas continually founded on themselves. If you don’t grasp a particular lesson, it may haunt you for months to come. Comprehending y-intercepts is an ideal example of topics that you will use in mathematics repeatedly

Let’s check out the basics regarding the y-intercept and show you some tips and tricks for working with it. Whether you're a math whiz or just starting, this preface will equip you with all the knowledge and tools you must possess to dive into linear equations. Let's dive right in!

What Is the Y-intercept?

To completely understand the y-intercept, let's think of a coordinate plane.

In a coordinate plane, two perpendicular lines intersect at a junction known as the origin. This junction is where the x-axis and y-axis join. 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 traveling across, and the y-axis is the vertical line going up and down. Every axis is counted so that we can locate points on the plane. The numbers on the x-axis increase as we shift to the right of the origin, and the numbers on the y-axis increase as we drive up from the origin.

Now that we have reviewed the coordinate plane, we can define the y-intercept.

Meaning of the Y-Intercept

The y-intercept can be taken into account as the starting point in a linear equation. It is the y-coordinate at which the coordinates of that equation intersects the y-axis. In other words, it signifies the value that y takes once x equals zero. After this, we will show you a real-life example.

Example of the Y-Intercept

Let's think you are driving on a long stretch of road with a single path going in respective direction. If you begin at point 0, where you are sitting in your vehicle right now, subsequently your y-intercept would be similar to 0 – given that you haven't moved yet!

As you start you are going the road and started gaining momentum, your y-intercept will increase unless it reaches some greater value when you arrive at a destination or stop to make a turn. Thus, when the y-intercept may not appear typically relevant at first glance, it can give details into how objects change over time and space as we shift through our world.

Therefore,— if you're always stranded attempting to get a grasp of this theory, keep in mind that just about everything starts somewhere—even your travel down that straight road!

How to Locate the y-intercept of a Line

Let's consider regarding how we can discover this value. To help with the process, we will create a summary of a some steps to do so. Thereafter, we will give you some examples to show you the process.

Steps to Locate the y-intercept

The steps to find a line that crosses the y-axis are as follows:

1. Locate the equation of the line in slope-intercept form (We will expand on this later in this tutorial), that should look as same as this: y = mx + b

2. Plug in 0 for x

3. Solve for y

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

Example 1

Find the y-intercept of the line explained by the equation: y = 2x + 3

In this instance, we can substitute in 0 for x and solve for y to find that the y-intercept is equal to 3. Therefore, we can say that the line crosses the y-axis at the point (0,3).

Example 2

As another example, let's consider the equation y = -5x + 2. In such a case, if we place in 0 for x one more time and work out y, we get that the y-intercept is equal to 2. Thus, the line goes through the y-axis at the point (0,2).

What Is the Slope-Intercept Form?

The slope-intercept form is a way of representing linear equations. It is the commonest form employed to depict a straight line in scientific and mathematical applications.

The slope-intercept formula 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 last portion, the y-intercept is the point where the line intersects the y-axis. The slope‌ is a scale of how steep the line is. It is the rate of change in y regarding x, or how much y shifts for each unit that x changes.

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


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

In this case, we can observe that m = -2 and b = 5. Consequently, the y-intercept is equal to 5. Therefore, we can state that the line intersects the y-axis at the coordinate (0,5).

We could take it a step higher to explain the slope of the line. In accordance with the equation, we know the slope is -2. Replace 1 for x and work out:

y = (-2*1) + 5

y = 3

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

Grade Potential Can Help You with the y-intercept

You will revise the XY axis repeatedly across your math and science studies. Theories will get more complicated as you move from solving a linear equation to a quadratic function.

The moment to peak your comprehending of y-intercepts is now prior you lag behind. Grade Potential offers experienced instructors that will guide you practice finding the y-intercept. Their personalized interpretations and practice questions will make a positive distinction in the outcomes of your test scores.

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