perpendicular/parallel lines
PERPENDICULAR LINES
Perpendicular lines are two lines that intercept, forming a 90° angle. In order for this to happen, the two lines must have an intercepting point, the place where the two lines meet. Also, the slope of one line must be the negative reciprocal of the other line, and when these are multiplied together, it should give a result of -1. In this example, one line has a slope of 2x, and the other one of -1/2x. This value id the negative reciprocal of 2, and if you multiply these products, you get -1. This proves that these lines are perpendicular to each other.
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PARALLEL LINES
Parallel lines are lines that will never touch each other, or intercept. In order for this to happen, the two lines must have exactly the same slope, and a different y-intercept, so they are not overlapping each other. In this example, one line has a y-intercept of 2, and the other one of -1. Their slope is 2x, which means 2 rise over 1 run.
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solving systems by graphing
When solving systems, you are determining the point of intersection. In this method, you are graphing the the two lines with the equations given, and then finding the intersecting point. The coordinates of the intersecting point are your answer, the x and y values.
*You can always check your answer by plugin in the x and y coodrinates of the intersecting point to the original equation, and see if these make sense and are accurate. |
solving systems by substitution
In this method, you are finding the value of one of the unknown values (either x or y) and you are going to plug it in one of the original equations. There are two equations of two lines, and each of these has a y value and a x value.
EXAMPLE Find the value of y
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Plug in the result into the original equation
ANSWER:
x = 2 y = 5 |
solving systems by elimination
So, y = -2
Now, we plug in this value into the original equation ANSWER
x = 1 y = -2 |
In this method, we are manipulating the equation, so that one of the unknown values "cancel out". Then we are finding the value for the other variable, and finally inserting in into the original equation by substitution, to find the value of the other value.
EXAMPLE: |
unit reflection
This was one of the hardest units for me. Specially because of the use of all these new methods to solve a system. Each of them is different in its own way, but for me that hardest one was elimination, since we had to manipulate and change the whole equation if it couldn't cancel out one of the variables. The easier method for me was the solving systems by graphing, since I was already familiarised with graphs and plotting lines. At the end of the unit, I still had problems with the perpendicular lines equation, so I had to review this many times, and it was a challenge. The parallel lines were simple and didn't require a lot of formulas or complicated processes. By the end of the unit, I was able to understand all of the methods to solve systems.
***REAL LIEE APPLICATION: Working with parallel lines made me realise of all the regular objects that can be parallel to each other. Also, graphs with two lines that intersect can show the relationship between the income of two companies, where the intersecting point meant what was what these had in common
***REAL LIEE APPLICATION: Working with parallel lines made me realise of all the regular objects that can be parallel to each other. Also, graphs with two lines that intersect can show the relationship between the income of two companies, where the intersecting point meant what was what these had in common