The y-intercept is found by simply plugging in a 0 for x in whatever function someone gives to you. The main job of the variable b is to tell you, at a glance, what y equals when x is 0, known as the y-intercept. This variable is the constant in the slope-intercept form, meaning that it is an unchanging number in the equation compared to the variables x and y. Of course, there is still the question of the last variable, b. Later, we will discuss the slope's importance and how you can use it in the slope-intercept form. When this is simplified, 3/2 is produced as the answer and the slope, m, for the function. You do this by using the equation (y2 - y1)/(x2-x1)=m where (x1, y1) and (x2, y2) are ordered pairs of a function.įor example, if you were given two ordered pairs, (3, 5) and (5, 8), of a single function, the equation would look like (8-5)/(5-3). You can find a line's slope or function by examining the rate of rise (how much the y value changes between two points) to run (how much the x value changes between those same two points). In other words, m describes how a function's ordered pairs change. Simply put, the slope is the rate at which the y values of a function grow or decrease in relation to the x values. The m variable, known as the "slope" in the slope-intercept form, is more complex compared to the other variables. The x telling them to go that many units right (or, if x is negative, left), and y telling them to go that many units up (or, if y is negative, down) when starting at the axis (where the two lines of a plane intersect). On this plane, ordered pairs act as directions for the person graphing the equation. Ordered pairs are important when it comes to plotting a function on a plane, which is a surface of two intersecting perpendicular lines, one horizontal and one vertical. This means that for every function, there are numerous unique ordered pairs.
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The ordered pair changes with the x value, as changing the input, in turn, changes the output. In the equation and example above, you would write the ordered pair as (3, 10) per the format. Ordered pairs simply put the x value (input) and y value (output) of a particular function together, formatted as (x, y). To show this input-output relationship between two values, you would write x and y values as something called an ordered pair. When you chose an x value, for example, 3, you would plug this in and do 3(3) + 1 to get 10, which is the output, y. Notice that there are now two variables with y replacing the question mark of the previous example. Say that someone presents you with another function, 3x + 1 = y. Instead, you allow the x value to determine what the output will be. Unlike x, you typically do not decide what the y value is. Now, just as the function "machine" has an input, it also has output, modeled by the variable y. The x value that you plugin can be any number, positive or negative.
![equation maker out of ordered pairs equation maker out of ordered pairs](http://i.ytimg.com/vi/oYYoQvgGcMg/maxresdefault.jpg)
When you plug x into the equation as a value, say, for the purpose of this example, 2, you would replace x with 2 and proceed to do 2 times 2, getting 4. For example, say you have the equation 2x = ? which is the "machine" in this case. You could say that x is the value that goes into a "machine" (which is, in this case, the function) to produce another value. The InputĪrguably the most important variable in the slope-intercept form is x. This is the input of the equation. In order to use the slope-intercept form effectively, it is crucial that you understand and can determine what these variables mean for the equation as a whole. The BasicsĪs mentioned previously, slope-intercept form, much like other forms used to model functions, uses variables to describe the meanings behind values in an equation. Even more, you can extract vast amounts of information from a single equation. Although this form, written as y=mx+b, can look odd and confusing due to its use of variables, it is easy to use with proper explanation and practice.
![equation maker out of ordered pairs equation maker out of ordered pairs](https://i.ytimg.com/vi/cXhpQZKlajQ/maxresdefault.jpg)
The slope-intercept form is the most common linear equation format.