Question

Complete the given table and draw a graph of the line ?

$x$	$0$	$1$	$2$	$3$
\[y = 3x + 1\]	$1$	4

Answer 1

Hint: In the given question, we are given a function in variables x and y. The given function represents a straight line on the Cartesian plane. A graph of a function f is the set of ordered pairs; the equation of graph is generally represented as $y = f\left( x \right)$, 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 first complete the given table by filling up the missing values of y by substituting the values of x in the function given to us. Then, we have to plot the graph for the given equation of line on the Cartesian plane.
These pairs or points are in the form of Cartesian form and the graph is the two-dimensional graph.
First, we have to find the missing values of y by using the graph equation \[y = 3x + 1\] for the given values of x.
So, Let us substitute the value of x as $2$. So, we get the value of y as
\[ \Rightarrow y = 3\left( 2 \right) + 1\]
$ \Rightarrow y = 6 + 1 = 7$
Now we consider the value of x as $3$, the value of y is
\[ \Rightarrow y = 3\left( 3 \right) + 1\]
\[ \Rightarrow y = 9 + 1\]
$ \Rightarrow y = 10$
Now, we complete the given table by filling up the missing values. So, we get,

$x$	$0$	$1$	$2$	$3$
\[y = 3x + 1\]	$1$	4	$7$	$10$

The graph plotted for the equation of the line using these points is represented below:

Note: The graph plotted is of two dimensional. The graph is plotted in x-axis versus y axis. 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.