Question

How do you graph the line $x - y = 4$ ?

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 solution:
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 $x - y = 4$. Let we substitute the value of x as $1$, $2$, $3$ and $4$.
Now we consider the value of x as $1$ , the value of y is
$ \Rightarrow y = x - 4$
$ \Rightarrow y = 1 - 4$
$ \Rightarrow y = - 3$
Now we consider the value of x as $2$, the value of y is
$ \Rightarrow y = x - 4$
$ \Rightarrow y = 2 - 4$
$ \Rightarrow y = - 2$
Now we consider the value of x as $3$, the value of y is
$ \Rightarrow y = x - 4$
$ \Rightarrow y = 3 - 4$
$ \Rightarrow y = - 1$
Now we consider the value of x as $4$, the value of y is
$ \Rightarrow y = x - 4$
$ \Rightarrow y = 4 - 4$
$ \Rightarrow y = 0$
Now we draw a table for these values we have

x	$4$	$3$	$2$	$1$
y	$0$	$ - 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.