Do you just have the topic of calculating the intersection point in math, but don’t know exactly how it works? Then you’ve come to the right place: In this article, we want to explain how you can do that Calculate the intersection of linear functions can. 🙂 The topic is assigned to the subject of mathematics and more precisely to the sub-topic of matrices.
What requirements must be met?
An intersection can only exist if both given lines have a different slope to have. That’s the only way they can cut each other. Two examples:
Example 1:
g: y = 2x + 1
h: y = 2x + 3
→ The straight lines have the same slope. So there is no intersection.
Example 2:
g: 2x + 1
h: 4x + 3
→ The straight lines have different gradients. There is an intersection.
In the next step we will show you how to calculate the point of intersection.
How do I calculate the intersection of two lines?
Once the condition that both given lines have different slopes is met, you can calculate their point of intersection. You can calculate it in three steps:
- Equate both functional equations.
- Solve equations for x.
- Substitute x into either function to calculate y.
We have prepared an example for you:
sample task
The following functional equations are given:
y = 0.5x – 1
y = -2x − 6
Calculate the intersection of both lines.
1. Equate functional equations.
y = y
or.
0.5x − 1 = −2x − 6
2. Solve the equation for x.
0.5x − 1 = −2x − 6 │+2x
0.5x + 2x − 1 = −2x + 2x − 6 │summarize
2.5x − 1 = − 6 │+1
2.5x − 1 + 1 = − 6 + 1 │summarize
2.5x = − 5 │/2.5
2.5x /2.5 = − 5 /2.5 │summarize
x = − 2
3. Substitute x into one of the functions to get y.
It doesn’t matter which function you plug x into, because both get the same result for y. So in the example we put −2 in the first equation:
y = 0.5x − 1
y = 0.5 * (−2) − 1 = −2
4. Result
The two straight lines intersect at Point S ( −2 │ − 2).
Both functional equations are drawn in the following figure so that you can also read off the point of intersection.