Y-Intercept - Meaning, Examples
As a learner, you are constantly seeking to keep up in class to avoid getting swamped by topics. As parents, you are constantly investigating how to motivate your kids to be successful in academics and furthermore.
It’s particularly essential to keep up in math reason being the ideas constantly build on themselves. If you don’t comprehend a particular lesson, it may hurt you in future lessons. Understanding y-intercepts is a perfect example of topics that you will revisit in mathematics repeatedly
Let’s go through the fundamentals regarding the y-intercept and show you some in and out for solving it. If you're a mathematical wizard or novice, this introduction will equip you with all the information and instruments you must possess to dive into linear equations. Let's dive right in!
What Is the Y-intercept?
To completely understand the y-intercept, let's picture a coordinate plane.
In a coordinate plane, two perpendicular lines intersect at a junction known as 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 written 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. Each axis is numbered so that we can locate points along the axis. The numbers on the x-axis grow as we move to the right of the origin, and the values on the y-axis increase as we move up from 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 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 portrays the value that y takes while x equals zero. After this, we will show you a real-world example.
Example of the Y-Intercept
Let's imagine you are driving on a long stretch of track with one path going in both direction. If you start at point 0, where you are sitting in your car this instance, subsequently your y-intercept will be similar to 0 – given that you haven't moved yet!
As you initiate traveling down the track and started gaining momentum, your y-intercept will increase unless it reaches some higher value once you arrive at a designated location or stop to make a turn. Therefore, while the y-intercept may not look typically relevant at first sight, it can offer insight into how things change eventually and space as we move through our world.
So,— if you're always puzzled attempting to understand this concept, bear in mind that just about everything starts somewhere—even your travel 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 help with the procedure, we will outline a handful of steps to do so. Thereafter, we will offer some examples to show you the process.
Steps to Discover the y-intercept
The steps to locate a line that intersects the y-axis are as follows:
1. Locate the equation of the line in slope-intercept form (We will dive into details on this afterwards in this article), that should appear as same as this: y = mx + b
2. Replace 0 in place of x
3. Solve for y
Now that we have gone over the steps, let's check out how this procedure will work with an example equation.
Example 1
Find the y-intercept of the line explained by the equation: y = 2x + 3
In this instance, we could plug in 0 for x and work out y to locate 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 additional example, let's consider the equation y = -5x + 2. In such a case, if we plug in 0 for x yet again and figure out y, we discover that the y-intercept is equal to 2. Therefore, the line goes through 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 mathematical and scientific uses.
The slope-intercept formula 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 went through in the previous section, the y-intercept is the point where the line crosses the y-axis. The slope is a scale of angle the line is. It is the unit of shifts in y regarding x, or how much y shifts for each unit that x changes.
Since we have reviewed the slope-intercept form, let's observe how we can employ it to discover the y-intercept of a line or a graph.
Example
Detect the y-intercept of the line state by the equation: y = -2x + 5
In this equation, we can see that m = -2 and b = 5. Therefore, the y-intercept is equal to 5. Consequently, we can conclude that the line crosses the y-axis at the coordinate (0,5).
We could take it a step further to depict the slope of the line. Based on the equation, we know the slope is -2. Place 1 for x and figure out:
y = (-2*1) + 5
y = 3
The solution tells us that the next point on the line is (1,3). Whenever x changed by 1 unit, y replaced by -2 units.
Grade Potential Can Help You with the y-intercept
You will revisit the XY axis repeatedly across your math and science studies. Ideas will get further complicated as you advance from solving a linear equation to a quadratic function.
The time to peak your grasp of y-intercepts is now prior you straggle. Grade Potential provides experienced instructors that will support you practice solving the y-intercept. Their tailor-made explanations and solve questions will make a positive difference in the results of your examination scores.
Anytime you think you’re lost or stuck, Grade Potential is here to guide!
