There are several ways to create a graph from a linear equation. A linear equation is an equation with two variables whose ordered pairs graph as a straight line. There are multiple ways to represent a linear relationship-a table, a linear graph, and there is also a linear equation.
In this case, the relationship is that the y-value is twice the x-value. You can think of a line, then, as a collection of an infinite number of individual points that share the same mathematical relationship. Look at how all of the points blend together to create a line. If you were to keep adding ordered pairs ( x, y) where the y-value was twice the x-value, you would end up with a graph like this. So if the rule of this pattern is that each y-coordinate is twice the corresponding x-value, then the ordered pairs (1.5, 3), (2.5, 5), and (3.5, 7) should all appear on the line too, correct? Look to see what happens. Once you know the pattern that relates the x- and y-values, you can find a y-value for any x-value that lies on the line. All of these x- and y-values follow the same pattern, and, when placed on a coordinate plane, they all line up. Notice that each y-coordinate is twice the corresponding x-value. In the table below, the x- and y-coordinates of each ordered pair on the graph is recorded.
Equation maker out of ordered pairs series#
These series of points can also be represented in a table. Applying the same logic, you may identify that the ordered pairs (6, 12) and (7, 14) would also belong if this coordinate plane were larger they, too, will line up with the other points. This makes sense because the point (5, 10) “lines up” with the other points in the series-it is literally on the same line as the others.
You probably identified that if this pattern continued the next ordered pair would be at (5, 10). Do you see any pattern to the location of the points? If this pattern continued, what other points could be on the line? Look at the five ordered pairs (and their x- and y-coordinates) below. Let’s start by looking at a series of points in Quadrant I on the coordinate plane. Now let's take 2^2 so x can be 2^0 or 2^1 or 2^2.A linear relationship is a relationship between variables such that when plotted on a coordinate plane, the points lie on a line. highest power of 3 is 3 and highest power of 5 is 3 Now atleast one of x and y, highest power of 2 is 2. Let two numbers x and y and their LCM is 2^2 * 3^3 * 5^3 Similarly, a, b and c can have powers of 7, such that at least one of them has the highest power of 7, in 19 ways.Ĭase 1- Number of ordered pairs when LCM is given But this will also contain cases when a, b, c will not have highest power of 17 so we have to remove those cases.Ĭases where highest power is in none of a, b and c is in 2 ways for each of a, b and c = > a, b and c cannot have highest power of 17 in 2 * 2 * 2 = 8 ways.Īt least one = total cases - cases when none of them has highest powerĪ, b and c can have powers of 17, such that at least one of them has the highest power of 17, in 27 - 8 = 19 ways. => a, b and c can have powers of 17 in 3 * 3 * 3 = 27 ways. So, powers of 17 till the maximum power available (17^0, 17^1, 17^2) and powers of 7 till the maximum power available 7 (7^0, 7^1, 7^2) will be distributed among a, b, c such that at least one of a, b, c has the highest power of 17 and at least one of them has the highest power of 7.Įach of a, b, c can have any one of three powers of 17 in 3 ways. Find the total number of ordered triplets (a, b, c) The LCM of three positive integers a, b, c is 119^2. Got the concept ? We will solve a question. If LCM of a and b is 2^3 * 3^3 then we will say that 2^3 will be in a or will be in b or will be in a and b both, same for 3^3.
So highest power should be distributed in atleast one of the number. so if highest power is same in both the number there will be no effect in LCM Now if we want to find LCM of 2^3 * 3^3 and 2^3 * 3^3 LCM will be still 2^3 * 3^3. Here we look for highest power of 2 and highest power 3. First let us understand some basic things about LCM
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