Y-Intercept - Definition, Examples
As a learner, you are constantly seeking to keep up in school to avoid getting engulfed by subjects. As parents, you are constantly investigating how to motivate your kids to prosper in academics and furthermore.
It’s especially critical to keep the pace in math because the concepts continually founded on themselves. If you don’t grasp 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 repeatedly
Let’s go through the foundation ideas about y-intercept and take a look at some in and out for working with it. Whether you're a math wizard or just starting, this small summary will enable you with all the things you need to learn and tools you must possess to tackle linear equations. Let's dive right in!
What Is the Y-intercept?
To completely comprehend the y-intercept, let's picture a coordinate plane.
In a coordinate plane, two perpendicular lines intersect at a point to be stated as the origin. This point 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 passing across, and the y-axis is the vertical line traveling up and down. Every single axis is numbered so that we can specific points on the plane. The numbers on the x-axis rise as we shift to the right of the origin, and the values on the y-axis rise as we drive 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 coordinates of that equation overlaps the y-axis. Simply put, it portrays the number that y takes while x equals zero. Next, we will show you a real-world example.
Example of the Y-Intercept
Let's assume you are driving on a long stretch of road with one lane going in respective direction. If you start at point 0, where you are sitting in your vehicle right now, subsequently your y-intercept would be similar to 0 – considering you haven't moved yet!
As you initiate traveling down the road and started gaining momentum, your y-intercept will rise until it reaches some greater value once you reach at a end of the road or halt to make a turn. Consequently, once the y-intercept may not seem typically applicable at first glance, it can provide insight into how things change over a period of time and space as we move through our world.
Hence,— if you're at any time stranded attempting to understand this theory, bear in mind that just about everything starts somewhere—even your journey through that long stretch of road!
How to Locate the y-intercept of a Line
Let's think about how we can find this value. To help with the method, we will make a synopsis of some steps to do so. Thereafter, we will offer some examples to show you the process.
Steps to Find 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 further ahead), that should look as same as this: y = mx + b
2. Substitute the value of x with 0
3. Calculate the value of y
Now that we have gone over the steps, let's see how this method will work with an example equation.
Example 1
Discover the y-intercept of the line explained by the formula: y = 2x + 3
In this instance, we could plug in 0 for x and figure out y to discover that the y-intercept is the value 3. Thus, we can say that the line intersects the y-axis at the coordinates (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 once again and solve for y, we get that the y-intercept is equal to 2. Thus, the line crosses the y-axis at the point (0,2).
What Is the Slope-Intercept Form?
The slope-intercept form is a method of representing linear equations. It is the most popular form employed to depict a straight line in scientific and mathematical 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 went through in the last section, the y-intercept is the coordinate where the line intersects 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 each unit that x changes.
Since we have revised the slope-intercept form, let's see how we can employ it to find 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 case, we can observe that m = -2 and b = 5. Consequently, the y-intercept is equal to 5. Therefore, we can state that the line intersects the y-axis at the point (0,5).
We can take it a step higher to depict the inclination of the line. In accordance with the equation, we know the inclination is -2. Plug 1 for x and calculate:
y = (-2*1) + 5
y = 3
The solution tells us that the next coordinate on the line is (1,3). Whenever x changed by 1 unit, y replaced by -2 units.
Grade Potential Can Support You with the y-intercept
You will revisit the XY axis repeatedly throughout your science and math studies. Ideas will get more complicated as you progress from solving a linear equation to a quadratic function.
The time to peak your grasp of y-intercepts is now before you lag behind. Grade Potential offers expert teacher that will support you practice solving the y-intercept. Their tailor-made explanations and practice problems will make a positive distinction in the results of your exam scores.
Whenever you believe you’re lost or stuck, Grade Potential is here to support!
