November 11, 2022

Y-Intercept - Definition, Examples

As a learner, you are continually seeking to keep up in school to avoid getting overwhelmed by subjects. As guardians, you are constantly searching for ways how to support your children to succeed in academics and after that.

It’s especially critical to keep up in math reason being the theories constantly build on themselves. If you don’t comprehend a particular topic, it may hurt you for months to come. Understanding y-intercepts is an ideal example of something that you will use in mathematics time and time again

Let’s check out the basics about y-intercept and take a look at some handy tips for working with it. Whether you're a mathematical wizard or novice, this small summary will provide you with all the information and tools you need to get into linear equations. Let's dive right in!

What Is the Y-intercept?

To fully understand 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 point 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 passing through, and the y-axis is the vertical line traveling up and down. Every axis is numbered so that we can locate points along the axis. The vales on the x-axis increase as we shift to the right of the origin, and the values on the y-axis increase as we shift 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 initial point in a linear equation. It is the y-coordinate at which the graph of that equation overlaps the y-axis. Simply put, it portrays the number that y takes once x equals zero. Next, we will explain a real-life example.

Example of the Y-Intercept

Let's assume you are driving on a straight track with one lane going in both direction. If you begin at point 0, where you are sitting in your vehicle this instance, subsequently your y-intercept will be similar to 0 – considering you haven't moved yet!

As you begin traveling down the track and picking up speed, your y-intercept will increase unless it reaches some higher number once you reach at a end of the road or stop to make a turn. Consequently, while the y-intercept may not look typically applicable at first look, it can offer insight into how objects transform over time and space as we move through our world.

So,— if you're ever puzzled attempting to understand this concept, keep in mind that almost everything starts somewhere—even your travel down that long stretch of road!

How to Locate the y-intercept of a Line

Let's consider regarding how we can find this value. To support you with the procedure, we will make a synopsis of some steps to do so. Thereafter, we will provide some examples to demonstrate the process.

Steps to Discover the y-intercept

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

1. Find the equation of the line in slope-intercept form (We will go into details on this later in this tutorial), that should appear similar this: y = mx + b

2. Plug in 0 for x

3. Work out y

Now that we have gone over the steps, let's check out how this process will function with an example equation.

Example 1

Discover the y-intercept of the line portrayed by the equation: y = 2x + 3

In this instance, we can plug in 0 for x and work out y to discover that the y-intercept is the value 3. Therefore, we can state that the line intersects the y-axis at the coordinates (0,3).

Example 2

As one more example, let's assume the equation y = -5x + 2. In this instance, if we substitute in 0 for x once again and work out y, we find that the y-intercept is equal to 2. Thus, 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 employed to express a straight line in mathematical and scientific subjects.

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

As we went through in the previous section, the y-intercept is the point where the line intersects the y-axis. The slope‌ is a measure of the inclination the line is. It is the rate of shifts in y regarding x, or how much y changes for every unit that x moves.

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


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

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

We could take it a step further to illustrate the inclination of the line. Founded on the equation, we know the inclination is -2. Place 1 for x and figure out:

y = (-2*1) + 5

y = 3

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

Grade Potential Can Support You with the y-intercept

You will revise the XY axis time and time again throughout your science and math studies. Theories will get further complicated as you move from working on a linear equation to a quadratic function.

The time to peak your grasp of y-intercepts is now prior you lag behind. Grade Potential offers expert instructors that will help you practice solving the y-intercept. Their tailor-made explanations and practice questions will make a positive distinction in the outcomes of your examination scores.

Whenever you feel stuck or lost, Grade Potential is here to assist!