November 11, 2022

Y-Intercept - Definition, Examples

As a student, you are constantly working to keep up in class to avoid getting swamped by topics. As parents, you are constantly investigating how to support your children to succeed in school and furthermore.

It’s particularly important to keep up in math reason being the ideas continually founded on themselves. If you don’t grasp a particular lesson, it may plague you in future lessons. Comprehending y-intercepts is an ideal example of theories that you will use in mathematics repeatedly

Let’s look at the fundamentals about y-intercept and take a look at some tips and tricks for working with it. If you're a mathematical whiz or novice, this small summary will provide you with all the things you need to learn and instruments you must possess to tackle 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 straight lines intersect at a section known as the origin. This junction 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 written 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. Each axis is numbered so that we can specific points along the axis. The counting on the x-axis rise as we move to the right of the origin, and the values on the y-axis increase as we shift up along the origin.

Now that we have gone over the coordinate plane, we can specify 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 coordinates of that equation intersects the y-axis. Simply put, it signifies the value that y takes once x equals zero. After this, we will show you a real-world example.

Example of the Y-Intercept

Let's suppose you are driving on a long stretch of highway with a single lane runnin in respective direction. If you begin at point 0, location you are sitting in your car right now, therefore your y-intercept would be equal to 0 – considering you haven't shifted yet!

As you initiate traveling down the road and picking up momentum, your y-intercept will rise until it archives some higher value once you arrive at a end of the road or halt to induce a turn. Thus, when the y-intercept may not appear particularly important at first glance, it can give knowledge into how objects transform over a period of time and space as we move through our world.

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

How to Discover the y-intercept of a Line

Let's consider about how we can find this value. To support you with the method, we will create a summary of a few steps to do so. Next, we will provide some examples to show you the process.

Steps to Locate the y-intercept

The steps to locate 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 appear something like this: y = mx + b

2. Substitute the value of x with 0

3. Solve for y

Now that we have gone through the steps, let's check out how this procedure will 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 replace in 0 for x and solve for y to locate that the y-intercept is equal to 3. Therefore, we can conclude that the line intersects 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 discover that the y-intercept is equal to 2. Thus, the line intersects the y-axis at the point (0,2).

What Is the Slope-Intercept Form?

The slope-intercept form is a technique of representing linear equations. It is the cost common kind used to depict a straight line in scientific and mathematical uses.

The slope-intercept equation 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 last portion, the y-intercept is the coordinate where the line crosses the y-axis. The slope‌ is a scale of the inclination the line is. It is the unit of deviation in y regarding x, or how much y changes for each unit that x shifts.

Considering we have went through the slope-intercept form, let's observe how we can utilize it to discover 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 observe that m = -2 and b = 5. Thus, the y-intercept is equal to 5. Therefore, we can conclude that the line goes through the y-axis at the point (0,5).

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

y = (-2*1) + 5

y = 3

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

Grade Potential Can Guidance You with the y-intercept

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

The time to peak your comprehending of y-intercepts is now before you straggle. Grade Potential gives experienced instructors that will support you practice finding the y-intercept. Their tailor-made explanations and practice problems will make a good distinction in the outcomes of your test scores.

Anytime you feel lost or stuck, Grade Potential is here to help!