An equation of line is a statement that indicates the form of a line and sets out its rules. In equations, any point on the line and is the slope of the line. The constant can be positive or negative (when). The graph for equation of line will have a y-intercept. Another way to represent the same straight line is by using different coordinates, which would result in standard equations. Standard equations allow one to remember information much more efficiently, as they make it possible to write down all properties using linear functions without ever multiplying by zero. To describe a point on a unit circle with an equation, one uses the standard equation.
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- A line can be defined as the intersection of two planes in space. A plane is an infinite flat surface with straight sides, and this means that once a line has been defined, it doesn’t move or change.
- Line equations are used to describe lines (or planes) that pass through any point on the Cartesian coordinate system, which includes points with x and y coordinates. The equation can also take into account additional parameters by using vectors, constants, trigonometric functions and exponents.
- All three forms use the same notation for differentiating between variables: uppercase letters indicate vectors while lowercase letters represent scalars (constants).
- No matter what form they take, equations of lines look like this:
y = mx + b
- In the equation, m represents the slope of a line. Slope can be recognized as an equation for a straight line drawn from a point on a graph to the point (0, 0). Vertical lines have no slope because they do not pass through any points at which x and y values change – only the value ‘1’ – so to find them, one simply divides -1 by itself, which gives one ‘undefined’. On the other hand, lines that don’t go all the way up or down are considered to have a horizontal slope. To find these lines, one would use either one of those infinite slopes: 1 or -1. Once they let m represent those functions in an equation of a straight line, one get this: y = mx + b
- This can be rewritten like this:
y – y = x(m) – b
- m is the slope, so an ‘m’ represents it. But there are two variables in this equation, so one has to use different variables to represent each one. For instance, let w represent the variable for the horizontal line and let u represent the variable for the vertical line.
- They look something like this:
u + w = one or u – w = one
- Suppose one compares them to their respective equations without using any letters. In that case, one will see that they’re identical, which means they could just leave out one of them when substituting form in one’s original equation. It would make things easier to write if one place the line with no slope first, which would leave one with this:
y – y = x(u) – w
- Now it’s time to substitute for u and w variables by multiplying each equation by respectively m and 1/m. You get these equations:
MX + (my) = (mu)x – w
MX + 1/m(my) = 1/mu x – MW
- Writing the final version of your equation of line you get:
mx + my – mu = mw y = x/m + m/(-mu) + b
- One can see that this equation can be rewritten in three forms, which can make things easier when plugging into an order of operations problem like this one. As the equation of line, there is an equation of circle also available.
Above here is a simple representation of the equation line. But if one access the Cuemath website, they can find further advanced information on the equation of a line, which can be very helpful for math geeks.