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

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

Let Point A be $\left(-2,{\displaystyle \frac{1}{2}}\right)$, Point B be $\left(4,5\right)$,Point C be $\left(2,{\displaystyle \frac{7}{2}}\right)$ 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.