Graphing - Standard Form of the Equation

Just a short explanation for what is meant by "standard form" of the equation of the line. We have been looking at line equations in the form of y=mx+b. However, you may be asked to express this in standard form.

The general notation for standard form is Ax + By = C, where A, B, and C are coefficients, and the x and y are the same variables we've been looking at but in a different position from what we recognize.

To express in standard form, you simply just rearrange the y = mx + b form such that you have x and y on the same side, equal to a number. Let's look at some examples:

Given that y = 3 x+ 5, standard form of this is 3x - y = (-5).

Given y = (1/2)x -15, standard form of this is (1/2)x - y = 15... also, if you don't want to ! have any fractions in your answer, you can multiply everything by the number in the denominator, such that we now get x - 2y = 30. Both expressions mean the same thing and will produce the same line. (In fact, convince yourself that no matter what you do to the equation, so long as you do it to both sides, the line is the same. eg. Multiply it all by 100, you get 100x-200y=30000... looks different, but it's not! Reduce it down and see for yourself!)

To go from standard form to the mx+b form, you may need to do a bit more math, but it's still quite straight forward.

Given 5x - 15y = 10, you just have to rearrange things to get y by itself on one side:
(-15y) = (-5x) + 10
y = (1/3)x - (2/3)...
and then you can see it is a line with slope 1/3 and y-intercept (-2/3).

Both types of equations mean the same thi! ng. They are just expressed differently, and y=mx+b gives imm! ediate i nformation about the line without having to do a lot of work. However, you should be able to use both forms interchangeably.

Also, from these equations, you should be able to tell that whenever you have an equation with 2 variables (x and y), and there aren't any exponents on either term, then you are dealing with a straight line. So while an equation in standard form may not immediately look like a straight line equation to you until it looks like y = mx + b, because it has an x and a y in it (without an exponent... exponents make the graph do cool things later), it is automatically a straight line.

(check this post for some additional pointers)

What is Standard Form