Question

How do you graph the line $2x - y = 4$ using a table of values ?

Answer 1

Hint: A graph of a function f is the set of ordered pairs; the equation of the 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:
To plot the given equation, we need a set of ordered pairs $(x,y)$ taking $y$ as a function of $x$, $y=f(x)$. These pairs are in the cartesian form and the graph is the two-dimensional graph.
To graph the given equation $2x - y = 4$, we $x$ and $y$ coordinates. We will take some $x$ values and substitute that in the given equation to get the corresponding $y$ values. So we will get (x,y) coordinate values to plot the required graph.
Writing of y in terms of x from the given equation, we get,
$ \Rightarrow y = 2x - 4$
Let we substitute the value of x as $0$, $1$, and $2$.
Step 1: Now we consider the value of x as $0$, the value of y is
$ \Rightarrow y = 2\left( 0 \right) - 4$
$ \Rightarrow y = - 4$
Step 2: Now we consider the value of x as $1$, the value of y is
$ \Rightarrow y = 2\left( 1 \right) - 4$
$ \Rightarrow y = - 2$
Step 3: Now we consider the value of x as $2$, the value of y is
$ \Rightarrow y = 2\left( 2 \right) - 4$
$ \Rightarrow y = 4 - 4$
$ \Rightarrow y = 0$
Now we draw a table for these values we have

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

The graph plotted for these point 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.
The standard equation of a straight line is $y=mx+c$, where $m$ is the slope of the straight line and $c$ is y-intercept.
Comparing the given equation with the standard equation,
$y=2x-4$
where slope$(m)=2$ and y-intercept$(c)=-4$.