Question

How do you graph the line $y = \dfrac{1}{3}x + 3$ ?

Answer 1

Hint: A graph of a function f is the set of ordered pairs; the equation of graph is generally represented as $y = f\left( x \right)$, 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 plot the graph for the given function. A graph of a function is a set of ordered pairs and it is represented as $y = f\left( x \right)$, 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 $y = \dfrac{1}{3}x + 3$. Let us substitute the value of x has $0$, $1$, $2$, and $3$. Now we consider the value of x as $0$, the value of y is
$y = \dfrac{1}{3}\left( 0 \right) + 3$
$ \Rightarrow y = 3$
Now we consider the value of x as $1$, the value of y is
$y = \dfrac{1}{3}\left( 1 \right) + 3$
$ \Rightarrow y = \dfrac{{10}}{3}$
Now we consider the value of x as $2$, the value of y is
$y = \dfrac{1}{3}\left( 2 \right) + 3$
\[ \Rightarrow y = \dfrac{{11}}{3}\]
Now we consider the value of x as $3$, the value of y is
$y = \dfrac{1}{3}\left( 3 \right) + 3$
$ \Rightarrow y = 1 + 3$
$ \Rightarrow y = 4$
Now we draw a table for these values we have

x	$0$	$1$	$2$	$3$
y	$3$	$\dfrac{{10}}{3}$	$\dfrac{{11}}{3}$	$4$

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.