Y-Intercept - Definition, Examples
As a student, you are constantly looking to keep up in class to avert getting overwhelmed by topics. As parents, you are constantly searching for ways how to motivate your children to succeed in school and after that.
It’s especially essential to keep up in mathematics because the theories continually build on themselves. If you don’t understand a specific topic, it may hurt you in next lessons. Understanding y-intercepts is the best example of topics that you will revisit in math time and time again
Let’s look at the fundamentals about y-intercept and show you some in and out for working with it. If you're a mathematical whiz or beginner, this small summary will equip you with all the information and tools you require to dive into linear equations. Let's get into it!
What Is the Y-intercept?
To entirely comprehend the y-intercept, let's imagine a coordinate plane.
In a coordinate plane, two straight lines intersect at a section to be stated as the origin. This junction 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 traveling through, 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 counting on the x-axis increase as we shift to the right of the origin, and the numbers on the y-axis grow as we shift up along 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 taken into account as the initial point in a linear equation. It is the y-coordinate at which the coordinates of that equation crosses the y-axis. Simply said, it portrays 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 path runnin in each direction. If you begin at point 0, where you are sitting in your vehicle this instance, therefore your y-intercept would be equivalent to 0 – given that you haven't moved yet!
As you start driving down the road and picking up speed, your y-intercept will rise until it archives some greater value once you reach at a end of the road or stop to induce a turn. Therefore, while the y-intercept might not look especially applicable at first sight, it can give insight into how things change eventually and space as we shift through our world.
So,— if you're ever stuck attempting to get a grasp of this theory, keep in mind that almost everything starts somewhere—even your trip through that long stretch of road!
How to Find the y-intercept of a Line
Let's think about how we can find this number. To guide with the process, we will outline a handful of steps to do so. Then, we will give you some examples to demonstrate the process.
Steps to Find the y-intercept
The steps to discover a line that goes through the y-axis are as follows:
1. Search for the equation of the line in slope-intercept form (We will expand on this afterwards in this article), which should look similar this: y = mx + b
2. Replace 0 in place of x
3. Figure out y
Now once we have gone over the steps, let's check out how this method will work 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 replace in 0 for x and figure out y to find that the y-intercept is the value 3. Consequently, we can state 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 instance, if we replace in 0 for x yet again 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 representing linear equations. It is the most popular kind employed to convey 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 saw in the last section, the y-intercept is the point where the line goes through the y-axis. The slope is a scale of the inclination the line is. It is the unit of change in y regarding x, or how much y shifts for every unit that x shifts.
Considering we have reviewed the slope-intercept form, let's check out how we can employ it to discover the y-intercept of a line or a graph.
Example
Detect 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. Consequently, the y-intercept is equal to 5. Therefore, we can conclude that the line crosses the y-axis at the point (0,5).
We can take it a step further to explain the slope of the line. Based on the equation, we know the slope is -2. Plug 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 changed by 1 unit, y changed by -2 units.
Grade Potential Can Help You with the y-intercept
You will revise the XY axis time and time again across your math and science studies. Concepts will get more difficult as you move from solving a linear equation to a quadratic function.
The moment to master your understanding of y-intercepts is now before you lag behind. Grade Potential provides expert teacher that will help you practice finding the y-intercept. Their customized explanations and solve questions will make a good distinction in the outcomes of your exam scores.
Anytime you think you’re lost or stuck, Grade Potential is here to assist!
