Calculate the intersection of two tangents
Don't get confused when it comes to calculating the intersection of two tangents. Here you only need knowledge from the intermediate level.
What you need:
- Intersection of two straight lines
- respectively. Equations with two unknowns
Tangents are only straight lines
- You have calculated two tangents for a given function and should now determine the point of intersection of these two. Even if this task looks difficult at first: Don't be fooled, because it is nothing more than calculating the intersection of two straight lines.
- Tangents, even if they have certain conditions regarding fulfilling the function are nothing more than straight lines of the form y = mx + b. If you have two different tangents, both are in this form.
- You can calculate the intersection of two straight lines by equating the two straight lines (intersection condition) and calculating the x-value of the intersection from this equation.
- You can obtain the y-value of the intersection point by inserting the x-value obtained into one of the two tangent equations. The other equation can be used for trial purposes.
- But be careful: If the two tangents are parallel (same slope), there is of course no point of intersection.
Determine the intersection of two functions for linear functions - this is how it works
You can usually draw the intersection of two linear functions ...
Intersection of two straight lines - a calculated example
The procedure is to be shown in detail using an example. For this the two tangents (Straight lines) y = 3x + 2 and y = -2x + 5 given. These two straight lines are not parallel, so they have an intersection point in two-dimensional space.
- Put the two straight lines equal. You get 3x + 2 = -2x + 5.
- You now have to solve this equation. You bring -2x (by adding) to the left and get 5x + 2 = 5. Now bring +2 (by subtracting it) to the right side. It follows 5x = 3 and by dividing you solve x = 3/5 = 0.6 as the x-value of the intersection of the two tangents.
- Now insert this calculated value into one of the two tangent equations. It follows that y = 3x + 2 = 3 * 0.6 + 2 = 1.8 + 2 = 3.8. So the point of intersection is S (0.6 / 3.8).
- The sample with the other tangent equation shows 3.8 = -2 * 0.6 + 5 = -1.2 + 5 = 3.8. The intersection of two straight lines was calculated correctly.
By the way: does the procedure remind you of anything? The calculation method is nothing more than two Equations with the two unknowns x and y, which in this case you solve with the equation method.
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