We Tutor All Subjects & Grade Levels - In Home And Online
November 11, 2022

Y-Intercept - Meaning, Examples

As a student, you are continually looking to keep up in school to avert getting overwhelmed by topics. As guardians, you are continually investigating how to encourage your children to prosper in academics and after that.

It’s specifically critical to keep up in math due to the fact that the theories continually founded on themselves. If you don’t understand a specific lesson, it may haunt you in future lessons. Comprehending y-intercepts is a perfect example of something that you will use in math over and over again

Let’s check out the foundation ideas regarding the y-intercept and take a look at some in and out for solving it. Whether you're a mathematical whiz or novice, this introduction will provide you with all the things you need to learn and instruments you require to get into linear equations. Let's get into it!

What Is the Y-intercept?

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

In a coordinate plane, two perpendicular lines intersect at a section called the origin. This section is where the x-axis and y-axis link. 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 going across, and the y-axis is the vertical line going up and down. Every single axis is counted so that we can specific points on the plane. The numbers on the x-axis rise as we shift to the right of the origin, and the values on the y-axis grow as we shift 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 taken into account as the starting point in a linear equation. It is the y-coordinate at which the graph of that equation intersects the y-axis. In other words, it represents the number that y takes while x equals zero. Next, we will illustrate a real-life example.

Example of the Y-Intercept

Let's suppose you are driving on a straight road with one lane going in respective direction. If you start at point 0, location you are sitting in your car right now, then your y-intercept would be equal to 0 – given that you haven't shifted yet!

As you start you are going the track and picking up momentum, your y-intercept will rise before it reaches some greater number once you reach at a end of the road or halt to induce a turn. Thus, when the y-intercept might not appear typically important at first look, it can offer knowledge into how things transform eventually and space as we move through our world.

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

How to Locate the y-intercept of a Line

Let's think about how we can find this value. To help with the procedure, we will outline a few steps to do so. Then, we will give you some examples to illustrate the process.

Steps to Locate the y-intercept

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

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

2. Plug in 0 for x

3. Figure out y

Now once we have gone over the steps, let's take a look how this method will function with an example equation.

Example 1

Discover 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 discover that the y-intercept is equal to 3. Consequently, we can say that the line intersects the y-axis at the coordinates (0,3).

Example 2

As another example, let's consider the equation y = -5x + 2. In such a case, if we substitute in 0 for x one more time and figure out y, we get that the y-intercept is equal to 2. Consequently, the line crosses the y-axis at the point (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 mathematical and scientific uses.

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 previous section, the y-intercept is the point 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 each unit that x shifts.

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

Example

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

In this instance, we can observe that m = -2 and b = 5. Thus, the y-intercept is equal to 5. Thus, we can conclude that the line intersects the y-axis at the point (0,5).

We could take it a step higher to illustrate the angle of the line. In accordance with the equation, we know the slope is -2. Replace 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). Whenever x changed by 1 unit, y changed by -2 units.

Grade Potential Can Support You with the y-intercept

You will review the XY axis time and time again during your math and science studies. Theories will get further difficult as you advance from solving a linear equation to a quadratic function.

The time to peak your grasp of y-intercepts is now before you lag behind. Grade Potential provides expert tutors that will support you practice finding the y-intercept. Their personalized interpretations and work out problems will make a good distinction in the results of your test scores.

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