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November 11, 2022

# Y-Intercept - Explanation, Examples

As a learner, you are continually seeking to keep up in class to avert getting overwhelmed by subjects. As guardians, you are continually investigating how to motivate your kids to be successful in academics and after that.

It’s particularly critical to keep up in math because the ideas always build on themselves. If you don’t grasp a particular lesson, it may plague you in next lessons. Comprehending y-intercepts is the best example of something that you will use in math repeatedly

Let’s check out the basics about y-intercept and show you some in and out for solving it. If you're a math whiz or beginner, this small summary will equip you with all the knowledge and tools you must possess to get into linear equations. Let's get into it!

## What Is the Y-intercept?

To entirely understand the y-intercept, let's picture a coordinate plane.

In a coordinate plane, two straight lines intersect at a point called 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 written like this: (0,0).

The x-axis is the horizontal line passing through, and the y-axis is the vertical line traveling up and down. Every axis is numbered so that we can identify a 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 rise as we move up along 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 coordinates of that equation intersects the y-axis. Simply said, it represents the number that y takes when x equals zero. Further ahead, we will illustrate a real-life example.

### Example of the Y-Intercept

Let's imagine you are driving on a straight highway with one path going in each direction. If you start at point 0, where you are sitting in your car this instance, therefore your y-intercept would be equal to 0 – considering you haven't moved yet!

As you start driving down the road and picking up speed, your y-intercept will increase unless it reaches some higher value when you reach at a destination or stop to make a turn. Therefore, while the y-intercept may not look particularly important at first look, it can provide insight into how objects change over time and space as we shift through our world.

Hence,— if you're at any time stranded attempting to get a grasp of this concept, keep in mind that just about everything starts somewhere—even your trip down that long stretch of road!

## How to Discover the y-intercept of a Line

Let's consider regarding how we can discover this value. To support you with the process, we will create a summary of a handful of steps to do so. Next, we will offer some examples to show you the process.

### Steps to Locate the y-intercept

The steps to find 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 something like this: y = mx + b

2. Substitute the value of x with 0

3. Figure out y

Now that we have gone over the steps, let's see how this process would work with an example equation.

### Example 1

Find the y-intercept of the line described by the formula: y = 2x + 3

In this example, we could plug in 0 for x and solve for y to locate that the y-intercept is the value 3. Thus, we can state that the line intersects the y-axis at the point (0,3).

### Example 2

As one more example, let's consider the equation y = -5x + 2. In such a case, if we plug in 0 for x once again and work out y, we discover that the y-intercept is equal to 2. Consequently, the line intersects the y-axis at the coordinate (0,2).

## What Is the Slope-Intercept Form?

The slope-intercept form is a way of depicting linear equations. It is the most popular kind used to convey a straight line in scientific and mathematical 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 saw in the last section, the y-intercept is the point where the line goes through the y-axis. The slope‌ is a measure 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 shifts.

Considering we have went through the slope-intercept form, let's observe how we can use it to locate the y-intercept of a line or a graph.

### Example

Find the y-intercept of the line described by the equation: y = -2x + 5

In this instance, we can see that m = -2 and b = 5. Therefore, the y-intercept is equal to 5. Consequently, we can say that the line crosses the y-axis at the point (0,5).

We can take it a step further to illustrate the slope of the line. Founded on the equation, we know the slope is -2. Plug 1 for x and work out:

y = (-2*1) + 5

y = 3

The answer tells us that the next point on the line is (1,3). Once x replaced by 1 unit, y replaced by -2 units.   