How To Use Our Slope Intercept Form Calculator
When you just know two different points that a line passes through, you can use our Slope Intercept Form Calculator to discover the equation of this line.
So, by using our simple Slope Intercept Form Calculator, you can easily discover the coefficients of the slope, the x-intercept, and even the y-intercept.
In order to use the Slope Intercept Form Calculator on the top of the page, you just need to add the coordinates of the two points that you already know. Then, just click on the Calculate button and the Slope Intercept Form Calculator will provide you with different results.
You will not only be able to discover the slope as well as the x-intercept and the y-intercept values.
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What Exactly Is The Slope Intercept Form?
Whenever you need to describe a line using math, you need to understand that it is always a linear equation or a straight line equation as it is also known. This means that the variables (x and y) won’t have any exponents.
The equation of any line is represented by: y = mx + b
This is a very important equation since it gives you two different values:
- the slope of the line (m), which is the gradient or the inclination of the line. In case the slope is a positive number, you can then say that the values of the y will increase as the values of the x increase. In case the slope or the m is a negative number, then you can say that the y decreases as the x increases.
- the y-intercept, which is the value of the y at which the line crosses the y-axis. In order to discover this number, you just need to assume that x = 0.
Calculating The Slope Intercept Manually
As we have already mentioned above, in order to calculate the slope intercept manually, you need to know two different points of the line. Let’s say that these points are A(x1,y1) and B(x2,y2).
In addition, you also know that in order to calculate the slope intercept, you need to use the equation of any line which is expressed by y = mx + b.
Use our Basic Calculator to do these simple calculations.
So, the first thing that you need to do is to replace the coordinates of both points in the equation of the line. You will end up with:
y1 = mx1 + b
y2 = mx2 + b
In order to use both coordinates of the point, you will need to subtract each one of the sides of the 2 equations like this:
y2 – y1 = m(x2 – x1)
Since you are trying to discover the slope, you need to:
m = (y2 – y1)/ (x2 – x1)
Since you already know the coordinates of both points, you will just need to replace them and you will get the slope.
In case you want to still discover the y-intercept, you will need to:
y1 = x1(y2 – y1) / (x2 – x1) + b
b = y1 – x1(y2 – y1) / (x2 – x1)
A Simple Example
Let’s say that you have two points P(3,7) and Q(15,9), and you want to find the slope intercept of the line.
You just need to use the equation of the line for each point:
– For P(3,7):
7 = 3m + b
– For Q(15,9)
9 = 15m + b
Subtracting both equations:
9 – 7 = m(15 – 3)
m = 2 / 12
m = 1/6
In case you also want to determine the y-intercept, you need to use the equation:
y1 = mx1 + b or y2 = mx2 + b
So, using the first one:
7 = 1/6 * 3 + b
b = 7 – (1/6 * 3 )
b = 7 – 1/2
b = 13/2 = 6.5
So, you can now say that the equation for the line is: y = 1/6m + 6.5