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Other forms of linear equations

Other forms of linear equations

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What is the name of this form of the equation of a straight line: (y2y1)=k(x2x1)(y_2-y_1)=k(x_2-x_1)?

Other forms of linear equations

​The equation of a straight line gives you all the information you need to draw a straight line in a coordinate system. The most common form of the equation of a straight line is this one. It is called the slope-intercept form. K is the gradient that represents the slope. M is the constant term that shows where the line crosses the Y axis.

But the equation of a straight line can be written in several ways. It can look like this, or like this, or like this. Or, like this. The first three describe the same line. The fourth one is somewhat special.

Let's look at them one at a time. ​ ​Here is the equation of a straight line in the point-slope form. It works like this. If you know one point and the slope of the line, you plug in the points X and Y coordinates in place of X1 and Y1 in the equation. You leave the X and Y without indices as two unknowns in the equation. We place K with the slope, two in this case. Solve the equation by isolating Y on the left side and you have a straight line in its usual slope intercept form again.

What about this form then? This form of the equation of a straight line is called the standard form. In the most general form, it looks like this. Notice that C does not indicate the Y intercept. If you encounter a linear equation in this form, don't panic.

Just solve the equation for Y. In other words, isolate Y on the left side to get back to the slope intercept form you're used to. ​ ​This one is the simplest of them all. You read the left side as F of X, this is just another way of pointing out that the equation is a function of X. In other words, that something changes because X changes. Other than that, it works just like the slope intercept form.

In this case, U is used instead of M, but it means the same thing. The letters are only labels, and as long as you know what they mean, you can use any letter. It could be g(t) = 2t + a. Or you could even use Greek letters α = 2β + γ. They have the same form, and they describe the same line. This one, however, is different.

It is also a linear equation, but it looks different. It has no Y value at all. This is a line where X always equals four, and that says nothing at all about Y. ​ ​What does such a line look like? Yes, it's a straight, vertical line which is parallel to the Y axis and crosses the X axis at four. At every point on this line, X equals four.

Y is absent, hence it is undefined. And this one, can you guess what is the equation of this line? Here, Y is always -2, and X is undefined. It is written like this. If you familiarize yourself with these forms, you can always draw a line in a coordinate system no matter in which form the equation is written.