My guess is that less than one percent of the algebra students in a school would be impressed with this equation. So, occassionally, I teach to the one percent. I got to thinking about this. This is a follow-up and add-on to johnnyb's excellent and important answer. One of the most important themes in Algebra 2 and higher-level classes is that of function transformation.
This theme runs throughout virtually every topic in those courses. Consider the following function types:. Now you might have noticed that "rescale it horizontally" is missing from the list above. Incidentally, this is one of the reasons why when students are learning about quadratic functions in vertex form they often mis-recognize "make it taller" as "make it skinnier".
Even for exponential functions, a horizontal rescaling can be absorbed into a change of the base, so you don't strictly speaking need them. It's really only for trigonometric functions that the horizontal scale factor plays a role that can't be accounted for by one of the other parameters. In high school, transformations are usually taught as a discrete topic, confined to an early chapter of Algebra 2 and only occasionally mentioned again, but I really think it is one of the most important throughlines of mathematics at the secondary and early postsecondary level.
In teaching university-level Calculus, for example, I will often begin the semester with a set of questions like this:. These are meant to be review problems, although students always struggle with questions Needless to say, every student can answer question 1. Most will use slope-intercept; a few will use point-slope form, and then rewrite their answer in slope-intercept form.
Then I show them that the function can be described as. We then spend the next couple of days approaching the rest of the problems using similar methods. This not only works well as a review of prerequisite material but also sets the stage for finding the equations of tangent lines, and much later Taylor series. The point-slope form is or has the potential to be students' first encounter with transformational thinking and lays the groundwork for these more advanced topics.
I think it is essential material for high school algebra. It can't be that important because I have never heard of it before and teach at university level. I believe textbooks will have some things because they provide an easy form of question rather than because they actually matter. Edit: The more I think about this, the more I agree with your teacher, in that I think it is unhelpful to teach both given that only one is needed.
What I mean is, the 'point-slope' equation is the same equation as the 'slope-intercept' equation. As such, I think it is unhelpful to teach one concept as if it is two different ones.
I believe that telling students incorrectly that these are different will encourage their natural tendency to think of the equation of a line as a string of characters, rather than a mathematical statement that is true for points on the line and false otherwise.
Also, emphasising the difference makes out that there is an important difference, when all the difference is is basic algebra. I would think this sends the message that the algebra is difficult and should be expected to be difficult already far too wide-spread an opinion.
Instead we should be teaching that the algebra is not difficult and is not the important feature. My suggestion, then, would be to teach both ways of writing the equation, showing that one or other may be more convenient depending on the information you have available, and can help in different ways to aid intuition. Emphasise that the two only differ by rearranging the formula, and that they can easily move between the two to get the viewpoint they find helpful. Before I get objections to this last point: if a student wrote something else I would consider it laziness, and if I saw anything else in a paper without reason I would be very surprised.
This can be a nice teaching moment on deriving formulas. Students who have a good grasp of the different forms of lines tend to do better when we introduce the conic sections, and I think that they're recognizing some of those similarities. It's similar to other common forms because those forms show the transformation form the origin for that family of curves. When teaching this in high school, it is helpful for some students to be encouraged to "get something on paper.
Tangent at a point. The currently most-voted answer mentions this, but not in the multivariable context. However, I will grant that for most high-school teachers in the US this will not seem the most compelling argument, since the small percentage of students who go on to this will probably survive no matter what version you use in 9th grade.
I see many good points here, addressing issues going forward. But I have a lower-level reason. They forget to give the equation of the line, which is what they were trying to find. When they use point slope form, it flows better.
I try to help students see why they would want to use each form, and how one form can transform into another.
As a student, I was taught all three major line formulas: point-slope, slope-intercept, and two-point and even exposed to the intercept, intercept oddity. I always devolved to just using point slope as it feels smaller and more intuitive.
Still to this day is how I think of lines. I think there is a physical intuition to it as well: initial condition and rate of change. But I was forced to be exposed to all of the equations. And I agree that, provided you remember them, the other equations work faster for problems suited to them. As for the teacher, of course, you should let him do things how he wants when you are the assistant and the class belongs to him.
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Create a free Team What is Teams? Learn more. Should I be teaching point-slope formula to high school algebra students? Ask Question. Asked 6 years ago. Active 3 months ago. Viewed 9k times. Improve this question. The Point-Slope equation is specifically designed to handle the trickiest type of questions, namely, how do you write an equation given two points? Remember, slope represents the steepness or the rate of change of our linear equation. In fact, this method is so straightforward, that you will find writing linear equations super easy!
And through this lesson, we will discover that the point-slope form definition is really just an extension of our beloved slope formula.
All we have to do is a little rearranging, as Math Is Fun so fittingly states, and we will see that point slope form is just the slope formula in disguise. However, m is undefined! So how are we supposed to plug that m into the equation? Let's start off with plugging on the x-coordinate and y-coordinate into the equation.
This gives us:. We are going to isolate for the letter m here. Now let's ask ourselves the question: when does m become undefined? It becomes undefined if we divide a number no. In other words,. See that the numerators of both fractions don't really tell us anything. However, if we match the denominators of the fractions, then we get:.
If you were to draw this line, you would get a vertical line that intersects the x-axis at The line is vertical because the run is 0. Hence the line rises infinitely, causing the line to go straight up. Now let's look at some questions which require us to use two points on a coordinate plane. Again, using the slope formula gives us the following:. So finding the slope from two points is actually pretty easy.
However, what if one of the points has a variable in it? What would that variable be? Let's look at an example. Notice that the point 2, a has the letter a in the y-coordinate. We are going to have to find this variable. Recall that to find the slope of the line, we use the slope equation. If we were to plug these into the slope formula , we will get:. Notice that within this equation, we can solve for a a a by isolating it. Multiplying both sides by 5 gives:.
Now what if a point contains the variable a in both the x-coordinate and y-coordinate? So plugging these into the slope formula gives us:.
The whole time we have been looking at slopes. However, what if I have to find the equation of a line in slope point form from the two points?
Notice that we can find the slope by using the slope formula with these two points. To find and , we can simply take one of the points given in the question.
Let's take the point 2, 6. Hence we can say that:. Now we know how to find an equation of a line when given to points, but what if we are given a graph? Now we need to find the slope. Recall that the slope formula is:. Our goal is to look at the graph and find out how much I need to run, and how much I need to rise to get to the next point on the line.
There are multiple ways to do this, but we will do it this way. Here we see that if we were to move 1 unit to the right and 2 units up, then that will lead us to the point 1,3. This point is on the line, so we know the amount of units we moved right and up are correct. We know that moving to the right by 1 means the run is equal to 1, and moving up 2 means the rise is 2. Hence, we conclude. If you are still having trouble visualizing the equation of a line, we recommend you to check the program at the bottom of this page.
This program lets you change the point and the slope of the line. With each change you make, you will get a different type of line. Play around with it and watch how the line changes!
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