This week, we learned about the different forms in which to represent an equation. There are 3 different kinds of these forms but some are used more or less than others, and I am going to focus on Point-Slope Formula. Each of these forms is related to linear equations, and are useful for graphing. We also discussed coincident lines, which will be explained more in depth, thought they are pretty simple.
Point Slope Formula
The kind of form I am going to focus on is point-slope form. This has its own formula, which is seen below. This is how you write equations using this formula, and just plug the numbers from your input/output charts into the corresponding places in the sentence. So basically, the slope of the formula is multiplied by x1-x2, and that is equal to y1-y2. During this equation, if we write out the slope in its regular form, it can help us more. Most of these forms rely on us being able to isolate the y variable, so algebra will also be needed to complete this.
How can you find the x and y intercepts using this method? Well, if we have an equation like the one written below, we can pick out which value is in the x2 spot, and the y2 spot, and use this to create an ordered pair to start at. Since the number before the x value is the slope, we can easily figure out multiple other ordered pairs by using this pattern and starting at the only known ordered pair.
Coincident Lines
What are coincident lines? These are lines that lie exactly on top of one another. It’s a pretty simple concept, but it is important and relative to when we look and observe the slope (rise/run) values of a line segment.