November 11, 2022

Y-Intercept - Definition, Examples

As a student, you are always looking to keep up in class to prevent getting engulfed by topics. As parents, you are always searching for ways how to motivate your kids to succeed in academics and after that.

It’s particularly important to keep up in math because the ideas constantly founded on themselves. If you don’t comprehend a particular lesson, it may haunt you in future lessons. Comprehending y-intercepts is the best example of something that you will revisit in mathematics repeatedly

Let’s go through the foundation ideas regarding the y-intercept and let us take you through some tips and tricks for working with it. Whether you're a mathematical whiz or novice, this preface will equip you with all the things you need to learn and instruments you require to get into linear equations. Let's dive right in!

What Is the Y-intercept?

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

In a coordinate plane, two straight lines intersect at a junction to be stated as the origin. This section 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 noted like this: (0,0).

The x-axis is the horizontal line passing across, and the y-axis is the vertical line going up and down. Each axis is numbered so that we can identify a points along the axis. The counting on the x-axis grow as we drive to the right of the origin, and the numbers on the y-axis increase as we move up along 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 thought of as the starting point in a linear equation. It is the y-coordinate at which the graph of that equation crosses the y-axis. In other words, it represents the value that y takes while x equals zero. After this, we will illustrate a real-life example.

Example of the Y-Intercept

Let's assume you are driving on a straight track with one lane runnin in both direction. If you start at point 0, where you are sitting in your vehicle this instance, then your y-intercept will be equal to 0 – given that you haven't shifted yet!

As you initiate traveling down the track and started gaining speed, your y-intercept will rise until it reaches some higher number once you arrive at a destination or stop to induce a turn. Thus, while the y-intercept might not look especially relevant at first glance, it can offer details into how objects transform eventually and space as we shift through our world.

Hence,— if you're at any time puzzled trying to comprehend this theory, keep in mind that almost everything starts somewhere—even your trip down that straight road!

How to Locate the y-intercept of a Line

Let's comprehend regarding how we can discover this number. To guide with the process, we will create a summary of a some steps to do so. Thereafter, we will give you some examples to illustrate the process.

Steps to Locate the y-intercept

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

1. Locate the equation of the line in slope-intercept form (We will expand on this further ahead), that should look something like this: y = mx + b

2. Substitute the value of x with 0

3. Solve for 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 can replace in 0 for x and figure out y to locate that the y-intercept is the value 3. Consequently, we can state that the line goes through the y-axis at the point (0,3).

Example 2

As additional example, let's take the equation y = -5x + 2. In this case, if we place in 0 for x once again and figure out y, we discover that the y-intercept is equal to 2. Consequently, the line intersects the y-axis at the point (0,2).

What Is the Slope-Intercept Form?

The slope-intercept form is a way of depicting linear equations. It is the commonest form utilized to convey a straight line in mathematical and scientific applications.

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 went through in the previous portion, the y-intercept is the coordinate where the line goes through the y-axis. The slope‌ is a measure of the inclination the line is. It is the unit of shifts in y regarding x, or how much y changes for every unit that x changes.

Since we have went through the slope-intercept form, let's observe how we can employ 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 instance, we can see that m = -2 and b = 5. Thus, the y-intercept is equal to 5. Therefore, we can state that the line intersects the y-axis at the point (0,5).

We could take it a step higher to depict the inclination of the line. Founded on the equation, we know the slope is -2. Plug 1 for x and work out:

y = (-2*1) + 5

y = 3

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

Grade Potential Can Support You with the y-intercept

You will revisit the XY axis time and time again during your math and science studies. Concepts will get more complicated as you progress from working on a linear equation to a quadratic function.

The time to master your understanding of y-intercepts is now prior you fall behind. Grade Potential offers expert tutors that will support you practice finding the y-intercept. Their tailor-made interpretations and work out problems will make a good difference in the results of your exam scores.

Whenever you believe you’re stuck or lost, Grade Potential is here to assist!