November 11, 2022

Y-Intercept - Definition, Examples

As a learner, you are always working to keep up in school to avert getting engulfed by subjects. As parents, you are continually searching for ways how to support your children to prosper in academics and after that.

It’s especially essential to keep up in math reason being the concepts always build on themselves. If you don’t understand a particular lesson, it may plague you for months to come. Understanding y-intercepts is an ideal example of theories that you will revisit in math repeatedly

Let’s look at the fundamentals about y-intercept and let us take you through some tips and tricks for solving it. If you're a math whiz or just starting, this small summary will provide you with all the information and tools you need to dive into linear equations. Let's dive right in!

What Is the Y-intercept?

To fully comprehend the y-intercept, let's think of a coordinate plane.

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

The x-axis is the horizontal line passing through, and the y-axis is the vertical line going up and down. Every axis is counted so that we can identify a points on the plane. The numbers on the x-axis increase as we shift to the right of the origin, and the values on the y-axis rise as we move 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 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 said, it signifies the value that y takes when x equals zero. Next, we will explain a real-life example.

Example of the Y-Intercept

Let's think you are driving on a straight highway with a single path runnin in each direction. If you start at point 0, location you are sitting in your vehicle right now, then your y-intercept will be equal to 0 – considering you haven't moved yet!

As you start you are going the track and started gaining speed, your y-intercept will rise unless it reaches some higher number once you reach at a destination or halt to make a turn. Therefore, while the y-intercept may not appear particularly applicable at first glance, it can offer details into how things change over a period of time and space as we travel through our world.

Hence,— if you're always stranded trying to get a grasp of this concept, keep in mind that nearly everything starts somewhere—even your trip down that long stretch of road!

How to Discover the y-intercept of a Line

Let's consider about how we can find this number. To help with the process, we will outline a some steps to do so. Next, we will offer some examples to demonstrate the process.

Steps to Discover the y-intercept

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

1. Find the equation of the line in slope-intercept form (We will dive into details on this afterwards in this article), which should look something like this: y = mx + b

2. Put 0 as the value of x

3. Work out y

Now that we have gone through the steps, let's see how this process will work with an example equation.

Example 1

Locate the y-intercept of the line described 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 equal to 3. Thus, we can conclude that the line intersects the y-axis at the point (0,3).

Example 2

As one more example, let's consider the equation y = -5x + 2. In this case, if we substitute in 0 for x once again and figure out y, we discover that the y-intercept is equal to 2. Therefore, 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 cost common form used to convey a straight line in scientific and mathematical subjects.

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 saw in the previous section, the y-intercept is the point where the line goes through the y-axis. The slope‌ is a measure of angle the line is. It is the rate of change in y regarding x, or how much y moves for every unit that x shifts.

Now that we have reviewed the slope-intercept form, let's check out how we can use it to locate the y-intercept of a line or a graph.

Example

Discover the y-intercept of the line signified 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. Consequently, we can say that the line goes through the y-axis at the coordinate (0,5).

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

y = (-2*1) + 5

y = 3

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

Grade Potential Can Guidance 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 advance from working on a linear equation to a quadratic function.

The time to peak your understanding of y-intercepts is now before you fall behind. Grade Potential provides expert instructors that will support you practice finding the y-intercept. Their tailor-made interpretations and practice questions will make a good difference in the outcomes of your examination scores.

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