Equations of lines come in several different forms. Two of those are:
Math Concepts equation in standard formgraphing lines in standard formgraphing standard formstandard form equationstandard form equation of a linestandard form graphingwrite an equation in standard form Numerist-Shaun When you have to determine the equation of a line from a graph, there are a couple of ways that you can express your answer.
All of these solutions, essentially, are exactly the same. That is, if you work backwards, you can take each form of the equation and draw the exact same line. The only thing that is different is the way that it looks, but the underlying mathematics are the same.
As I mentioned in my last post, one of the more common ways of expressing an equation of a line is in slope-intercept form.
In this post, I am going to show you how to write an equation in standard form. By now, you are probably familiar with this easy-to-remember equation: This is the slope-intercept equation, where x and y form a coordinate on the line, m represents the slope of the line think: However, you may instead be asked to express this in standard form, or write a standard form equation.
In simple terms, this basically means to write your equation with the x and y variables and their coefficients grouped together on one side of the equals sign, with the constant term on the other side.
Perhaps seeing the general version of this equation will be more helpful than words.
If we say that x and y are the variables of the graph, and A, B, and C are coefficients, we can assemble these in the following way to show a generic equation in standard form: You can hopefully notice that this looks very similar to the slope-intercept equation of the line, but things seem to be slightly rearranged.
That is the key point that I want you to be able to take away from this post — all of these versions are very similar and are built from the same numbers, but they are just written in a different arrangement from what you may be able to immediately recognize.
So, really, being able to write an equation in standard forms comes down to your ability to properly reorganize the terms. As you can see, in this basic example, it was just a matter of grouping the x and y terms on the same side, while leaving the constant value on the other side.
Note that I wrote the x value first, followed by the y term, as required by the standard form. You will also often be asked to specifically identify what the A, B, and C values are, so in this case, A is -5, B is 1 assumed, since there is no explicitly given coefficientand C is 2.
Alternately, you would also be correct if you did the rearrangement the other way — that is, subtracted y from both sides, and then subtracted 2 from both sides. That would give you: In this case, A is 5, B is -1, and C is Either of these two solutions are correct.
Technically, I prefer to have an answer where the x value has a positive coefficient, so this second version is probably the one that I would use.
What about a slightly more complicated-looking starting equation? In this case, the standard form equation of a line has the following values for its coefficients:Here you'll be shown how to take the equation of a circle, and convert it into standard form.
Also, it will be explained just what standard form is, while running through the process of conversion. You'll be able to use techniques to quickly work off the numbers on the equation, one by one, until it's simplified enough to understand. In this post, I am going to show you how to write an equation in standard form.
By now, you are probably familiar with this easy-to-remember equation: This is the slope-intercept equation, where x and y form a coordinate on the line, m represents the slope of the line . How do you write the standard form of a line given x-intercept=3, y-intercept=2?
Algebra Forms of Linear Equations Write an Equation Given Two Points 1 Answer. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.. If you know two points that a line passes through, this page will show you how to find the equation of the line.
Jan 07, · When given a linear equation in standard form, to graph the equation, we first rewrite the linear equation in slope intercept form, (i.e.
in the form y = mx + c, where m is the slope and c is the. Sep 14, · Learn how to write the equation of a line in a point-slope form. The equation of a line is such that its highest exponent on its variable(s) is 1.
(i.e. there are no exponents in its variable(s)).