Y-Intercept - Meaning, Examples
As a learner, you are continually looking to keep up in class to avoid getting overwhelmed by subjects. As guardians, you are constantly searching for ways how to motivate your children to prosper in academics and beyond.
It’s especially essential to keep up in math due to the fact that the theories always build on themselves. If you don’t understand a specific topic, it may haunt you in next lessons. Understanding y-intercepts is an ideal example of something that you will use in mathematics time and time again
Let’s look at the foundation ideas regarding the y-intercept and let us take you through some handy tips for solving it. If you're a math wizard or just starting, this introduction will provide you with all the knowledge and tools you must possess to tackle 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 straight lines intersect at a junction to be stated as the origin. This section 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 going 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 numbers on the x-axis increase as we drive to the right of the origin, and the values on the y-axis grow as we move up from the origin.
Now that we have revised the coordinate plane, we can determine the y-intercept.
Meaning of the Y-Intercept
The y-intercept can be considered as the starting point in a linear equation. It is the y-coordinate at which the graph of that equation intersects the y-axis. Simply said, it represents the number that y takes once x equals zero. After this, we will show you a real-life example.
Example of the Y-Intercept
Let's suppose you are driving on a straight road with a single path runnin in respective direction. If you start at point 0, location you are sitting in your car right now, therefore your y-intercept will be equal to 0 – given that you haven't moved yet!
As you begin traveling down the road and started gaining speed, your y-intercept will increase unless it archives some greater value when you arrive at a end of the road or stop to make a turn. Consequently, while the y-intercept might not look especially important at first look, it can give details into how things change over a period of time and space as we move through our world.
Hence,— if you're ever stranded trying to comprehend this concept, bear in mind that nearly everything starts somewhere—even your travel through that straight road!
How to Discover the y-intercept of a Line
Let's think about how we can locate this value. To support you with the procedure, we will create a summary of a few steps to do so. Thereafter, we will give you some examples to illustrate the process.
Steps to Find the y-intercept
The steps to discover a line that goes through the y-axis are as follows:
1. Locate the equation of the line in slope-intercept form (We will dive into details on this further ahead), which should look similar 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 see how this method will work with an example equation.
Example 1
Find the y-intercept of the line described by the equation: y = 2x + 3
In this instance, we can replace in 0 for x and figure out y to find that the y-intercept is equal to 3. Consequently, we can say that the line crosses the y-axis at the coordinates (0,3).
Example 2
As additional example, let's consider the equation y = -5x + 2. In this case, if we plug in 0 for x yet again and figure out y, we find that the y-intercept is equal to 2. Consequently, the line crosses the y-axis at the coordinate (0,2).
What Is the Slope-Intercept Form?
The slope-intercept form is a technique of depicting linear equations. It is the most popular kind employed to express 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 how steep the line is. It is the rate of change in y regarding x, or how much y moves for every unit that x changes.
Now that we have reviewed the slope-intercept form, let's observe how we can use it to discover the y-intercept of a line or a graph.
Example
Discover the y-intercept of the line described by the equation: y = -2x + 5
In this case, we can see that m = -2 and b = 5. Thus, the y-intercept is equal to 5. Therefore, we can say that the line intersects the y-axis at the coordinate (0,5).
We could take it a step further to explain the inclination of the line. Founded on the equation, we know the inclination is -2. Replace 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). Whenever x replaced by 1 unit, y changed by -2 units.
Grade Potential Can Guidance You with the y-intercept
You will review the XY axis repeatedly throughout your math and science studies. Theories will get more complicated as you advance from working on a linear equation to a quadratic function.
The moment to peak your grasp of y-intercepts is now prior you fall behind. Grade Potential gives experienced instructors that will guide you practice finding the y-intercept. Their personalized explanations and work out problems will make a good difference in the results of your examination scores.
Whenever you feel stuck or lost, Grade Potential is here to help!
