Question

Draw the graph of multiples of 3.

Answer 1

Hint: We will form such an equation which will give only those points which will be the multiples of 3. We can also draw the graph containing these types of points. We will do this in order to solve the question.

Complete step-by-step answer:
For making the graph of multiples of 3 we must have those points which correspond to the multiple of 3. For that we will consider the points that are the multiples of 3. By multiple of 3 we mean those numbers that are a product of any number along with the number 3. For example, if we take a number 9 then we see that the number 9 is a multiple of 3 as it is a product of any number and 3. We can also consider this by the term factors with the remembrance of the basic difference between factors and multiples.
The difference between them is that factors are those numbers that we multiply to get a number where as a multiple is that number which we multiply to get the required number. This can be numerically written as, multiple = any number $\times$ factor. For example, if we have 9 then nine has factors as 1, 3 and 9. And the numbers which divide 9 are 1, 3 and 9. Therefore, we get that 1, 3 and 9 will be the multiples of 3.
Now, we will consider an equation like this y = 3x. Here, x contains the numbers that belong to integers. As we can clearly see that y = 3x then it explains that whatever number the variable y will get will be a multiple of three automatically. For drawing the graph we need points for plotting it. Consider the equation y = 3x. Now we will make the substitutions one by one. Put x = 0 we will get y = 0. Put x = 1 we will get y = 3. Therefore we get the points as (0, 0) and (1, 3). Similarly in this manner we will get points as (2, 6), (3, 9) and so on.
The required graph for the question is given below.

Note: We can also put negative points like x = - 1 and we will get y = - 3 which is also a multiple of 3. But one thing should be kept in mind that there will not be any substitutions of fractions. For example we will not substitute any complex points or irrational points in the equation. We are free to substitute any point in x and obtain the values of y corresponding to it, but if we put any point in y and find values for x, it will be difficult.