How many lines go through two points
Linear function through 2 points
This article is about using two points to determine a linear function / straight line. This is shown by a few examples. This article is part of our Mathematics section.
Sometimes you look for a role in a math class. Then different points are given and a function is to be determined that runs exactly through these points. To understand the next few sections you should know what a linear function is and how to solve a linear system of equations.Show:
Even / linear function through 2 points
A straight line or a linear function is described with f (x) = y = mx + b. The variables m and b are unknown. To determine this we need two points. With this we set up two equations and solve the linear system of equations to determine m and b. This will now be shown by means of examples.
On the following graphic you can see a linear function. We are looking for a mathematical description of this process. To do this, we first read two points on the graphic. This would be for example P1 (0 | 0) and P2 (1 | 2). So we have two points, each with an X value and a Y value. We put both points in y = mx + b. We thus get two equations:
- P1: 0 = m * 0 + b
- P2: 2 = m * 1 + b
From the first equation we see that b = 0. If we plug this into the second equation, we still get m = 2. So after plugging in y = mx + b we get:
There are two points with P1 (2 | 3) and P2 (5 | 6). What is the corresponding linear function?
Solution: We insert both points in y = mx + b and then solve the linear system of equations.
- P1: 3 = m * 2 + b
- P2: 6 = m * 5 + b
We convert the first equation to b:
And plug this into the second equation:
- 6 = 5m + b
- 6 = 5m + 3 - 2m
- 3 = 3m
- m = 1
With m = 1 we go into the first equation:
- 3 = 2m + b
- 3 = 2 x 1 + b
- 3 = 2 + b
- b = 1
With b = 1 and m = 1 we get:
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