Y-Intercept - Meaning, Examples
As a learner, you are always looking to keep up in school to avert getting swamped by subjects. As guardians, you are continually investigating how to encourage your kids to prosper in academics and after that.
It’s specifically important to keep up in math reason being the concepts continually founded on themselves. If you don’t comprehend a particular topic, it may hurt you in future lessons. Understanding y-intercepts is an ideal example of something that you will use in mathematics over and over again
Let’s go through the fundamentals about y-intercept and take a look at some tips and tricks for working with it. Whether you're a math wizard or novice, this preface will equip you with all the information and tools you must possess to tackle linear equations. Let's jump directly to it!
What Is the Y-intercept?
To fully comprehend the y-intercept, let's imagine a coordinate plane.
In a coordinate plane, two straight lines intersect at a section called the origin. This junction 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 traveling through, and the y-axis is the vertical line traveling up and down. Each axis is numbered so that we can identify a points on the plane. The vales on the x-axis increase as we shift to the right of the origin, and the values on the y-axis increase as we drive up from 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 considered as the starting point in a linear equation. It is the y-coordinate at which the graph of that equation overlaps the y-axis. Simply put, it portrays the value that y takes once x equals zero. Next, we will show you a real-world example.
Example of the Y-Intercept
Let's imagine you are driving on a straight highway with a single path going in respective direction. If you start at point 0, location you are sitting in your car this instance, subsequently your y-intercept would be similar to 0 – considering you haven't shifted yet!
As you begin traveling down the track and picking up speed, your y-intercept will increase until it reaches some greater number once you arrive at a designated location or halt to induce a turn. Consequently, once the y-intercept may not appear particularly applicable at first glance, it can provide insight into how objects change over time and space as we shift through our world.
Therefore,— if you're ever stuck attempting to comprehend this concept, keep in mind that nearly everything starts somewhere—even your trip through that long stretch of road!
How to Discover the y-intercept of a Line
Let's comprehend about how we can find this value. To support you with the method, we will make a synopsis of handful of steps to do so. Next, we will offer some examples to illustrate the process.
Steps to Discover the y-intercept
The steps to discover 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 further ahead), that should look something like this: y = mx + b
2. Put 0 as the value of x
3. Calculate the value of y
Now that we have gone through the steps, let's take a look how this process will function with an example equation.
Example 1
Find the y-intercept of the line described by the equation: y = 2x + 3
In this example, we can replace in 0 for x and work out y to locate that the y-intercept is the value 3. Thus, we can state that the line goes through the y-axis at the point (0,3).
Example 2
As additional example, let's assume the equation y = -5x + 2. In such a case, if we replace in 0 for x one more time and figure out y, we get 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 technique of depicting linear equations. It is the commonest kind 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 checked in the last portion, the y-intercept is the point where the line crosses 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 changes for each unit that x changes.
Now that we have reviewed the slope-intercept form, let's see how we can employ it to discover the y-intercept of a line or a graph.
Example
Find the y-intercept of the line signified by the equation: y = -2x + 5
In this equation, we can see that m = -2 and b = 5. Thus, the y-intercept is equal to 5. Therefore, we can say that the line goes through the y-axis at the coordinate (0,5).
We can take it a step further to depict the angle of the line. Based on the equation, we know the slope 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). When x replaced by 1 unit, y replaced by -2 units.
Grade Potential Can Help You with the y-intercept
You will revisit the XY axis time and time again throughout your science and math studies. Concepts will get further complicated as you progress from solving a linear equation to a quadratic function.
The time to master your comprehending of y-intercepts is now prior you straggle. Grade Potential provides experienced tutors that will help you practice finding the y-intercept. Their customized explanations and practice problems will make a positive distinction in the results of your exam scores.
Anytime you feel stuck or lost, Grade Potential is here to guide!
