Question

How do you graph \[y = \left( {\dfrac{1}{2}} \right)x\] by plotting points?

Answer 1

Hint: A graph of a function f is the set of ordered pairs; the equation of graph is generally represented as \[y = f(x)\] , where x and f(x) are real numbers. We substitute the value of x and we determine the value of y and then we mark the points in the graph and we join the points.

Complete step-by-step answer:
Here in this question, we have to plot the graph for the given function. A graph of a function is a set of ordered pairs and it is represented as \[y = f(x)\] , where x and f(x) are real numbers. These pairs are in the form of cartesian form and the graph is the two-dimensional graph.
First, we have to find the value of y by using the graph equation \[y = \left( {\dfrac{1}{2}} \right)x\] . Let us substitute the value of x has -6, -4, -2, 0, 2, 4, and 6. Here we have chosen the points which are multiples of two, because in the equation of a graph we have a fraction and the denominator contains 2.
Now we consider the value of x as -6, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{2}} \right)( - 6) \\
   \Rightarrow y = - 3 \;
 \]
Now we consider the value of x as -4, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{2}} \right)( - 4) \\
   \Rightarrow y = - 2 \;
 \]
Now we consider the value of x as -2, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{2}} \right)( - 2) \\
   \Rightarrow y = - 1 \;
 \]
Now we consider the value of x as 0, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{2}} \right)(0) \\
   \Rightarrow y = 0 \;
 \]
Now we consider the value of x as 2, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{2}} \right)(2) \\
   \Rightarrow y = 1 \;
 \]
Now we consider the value of x as 4, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{2}} \right)(4) \\
   \Rightarrow y = 2 \\
 \]
Now we consider the value of x as 6, the value of y is
 \[
   \Rightarrow y = \left( {\dfrac{1}{2}} \right)(6) \\
   \Rightarrow y = 3 \;
 \]
Now we draw a table for these values we have

x	-6	-4	-2	0	2	4	6
y	-3	-2	-1	0	1	2	3

The graph plotted for this point is represented below:

Note: The graph is plotted x-axis versus y axis. The graph is two dimensional. By the equation of a graph, we can plot the graph by assuming the value of x. we can’t assume the value of y. because the value of y depends on the value of x. Hence, we have plotted the graph.