Slope intercept calculator is used to find the equation of a certain line for any two given points that the line passes through. With it, you can find the slope’s coefficient, the y-intercept, and the x-intercept using the required slope intercept formula. The article covers how to use the calculator along with other concepts related to slope intercepts.
How to use the slope intercept form calculator?
This slope intercept calculator is a simple and easy online tool which you can use to find the slope, angle, and distance. Instead of using the slope intercept formula to calculate manually, this online tool does the work for you. Here are the steps to follow for this calculator:
- For this calculator, you need to input four different values namely x1, y1, x2, and y2.
- After inputting these values, the slope intercept form calculator automatically generates for you the values of the Slope, Angle, and Distance.
- It also gives you the values of Δx and Δy.
What is slope intercept form in math?
Before using this slope or y intercept calculator, you must understand what a slope intercept form is in math. Mathematically, you can describe any line in a given plane as the relationship between the y-axis and the x-axis of the individual points which contribute to that line. In this case, the slope refers to the line’s gradient or inclination.
This slope intercept form describes how much y changes for any fixed change that occurs in x. If you have a positive value, this means that the y values increase as the x increases. If you have a negative value, this means that the y values decrease as the x increases.
What’s the point slope formula?
If you want to solve for the value manually instead of using a slope intercept form calculator, use the proper point slope formula. To understand the calculation correctly, follow these steps:
- For the first point, let’s assign its coordinates as (x1, y1) while the coordinates of the second point are (x2, y2).
- Using the equation, substitute the values:
y₁ = mx₁ + b
y₂ = mx₂ + b
- After this, subtract your first equation from the second one:
y₂ – y₁ = m(x₂ – x₁)
- The last step is to divide both sides of the equation by (x₂ – x₁) to obtain the slope:
m = (y₂ – y₁) / (x₂ – x₁)
After solving for the slope, you can take it further in order to obtain the y intercept:
y₁ = x₁(y₂ – y₁)/(x₂ – x₁) + b
b = y₁ – x₁(y₂ – y₁)/(x₂ – x₁)
Then you can check whether you solved the slope correctly or not using the slope intercept calculator or the y intercept calculator.
What is an example of a y intercept?
When you have an x value equal to zero, the corresponding y-value is the y intercept. To help you understand this better, let’s look at the y intercept in the context of word problems. You can think of the y intercept as the starting value.
For an exercise that’s time-based, this refers to the value when you began reading or when you began keeping track of the time and all the changes related to it. In sociology, the y intercept may refer to the population at the time when sociologists began recording the said population.
For instance, if these sociologists took the measurements from the year 1996, then the y intercept corresponds to “the population in 1996” while x=o corresponds to “the year 1996.”
How to find y intercept?
In an equation, the y-intercept refers to the point where the equation’s graph intersects with the y-axis. There are different ways to find an equation’s y intercept but since this article is all about the slope intercept, we’ll use this method. Here are the steps to follow:
- First, write down the values for the point and the slope. The slope refers to the value which tells you the steepness of the line. For this, you would also have the (x,y) coordinates of a single point along the given graph.
- Let’s assume that you have a straight line with a slope 2 and the point (3,4). With this information, you can find the y intercept by following the next few steps.
- The next thing to do is to learn the equation’s slope-intercept form. Remember that you can write any given straight line as an equation: y = mx + b. In this form of the equation, the m variable refers to the slope while the b variable refers to the y intercept.
- In this equation, substitute the value for the slope. Therefore, when you’re writing the slope-intercept equation, write the slope of the line in place of m. In our example:
y = mx + b
m is the slope = 2
y = 2x + b
- Now it’s time to replace the y and x coordinates of your point. As long as you have the values of the coordinates of any single point on the given line, you can substitute these values for the y and x coordinates in the equation. So in your equation, this is:
In our example, the coordinates of the point of the line are (3,4) which means that x = 3 and y = 4.
Substitute these values for the x and y values in the equation: 4 = 2(3) + b.
- The next step to take is to solve for b or the y intercept. As you can see, b is the only variable which remains in your equation. Therefore, all you have to do is rearrange the variables to find the y intercept. Starting with 4 = 2(3) + b, rearrange the equation in a few steps:
4 = 6 + b
4 – 6 = b
-2 = b or the y intercept
- Finally, write the value you obtained as a coordinate point. Remember that the y intercept refers to the point where the given line intercepts with the y-axis.