Question

How do you graph the line $3x - 4y = - 8$ ?

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 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 $3x - 4y = - 8$. Let we substitute the value of x has$0$, $2$, $3$ and $\left( { - 2} \right)$.
Now we consider the value of x as $0$, the value of y is
$ \Rightarrow y = \left( {\dfrac{{3x + 8}}{4}} \right)$
$ \Rightarrow y = \left( {\dfrac{{3\left( 0 \right) + 8}}{4}} \right)$
$ \Rightarrow y = 2$
Now we consider the value of x as $2$, the value of y is
$ \Rightarrow y = \left( {\dfrac{{3x + 8}}{4}} \right)$
$ \Rightarrow y = \left( {\dfrac{{3\left( 2 \right) + 8}}{4}} \right)$
$ \Rightarrow y = \dfrac{7}{2}$
Now we consider the value of x as $4$, the value of y is
$ \Rightarrow y = \left( {\dfrac{{3x + 8}}{4}} \right)$
$ \Rightarrow y = \left( {\dfrac{{3\left( 4 \right) + 8}}{4}} \right)$
$ \Rightarrow y = 5$
Now we consider the value of x as $\left( { - 2} \right)$, the value of y is
$ \Rightarrow y = \left( {\dfrac{{3x + 8}}{4}} \right)$
$ \Rightarrow y = \left( {\dfrac{{3\left( { - 2} \right) + 8}}{4}} \right)$
$ \Rightarrow y = \dfrac{1}{2}$
Now we draw a table for these values we have

x	$ - 2$	$4$	$2$	$0$
y	$\dfrac{1}{2}$	$5$	$\dfrac{7}{2}$	$2$

Let Point A be $\left( { - 2,\dfrac{1}{2}} \right)$, Point B be $\left( {4,5} \right)$,Point C be $\left( {2,\dfrac{7}{2}} \right)$ and Point D be $\left( {0,2} \right)$.
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.