Question

How do you graph the line $x = - 6y$ ?

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. So, we will first form a table of the points that lie on the given line and then plot those points and the line passing through them.

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 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 $x = - 6y$. Let us substitute the value of x as $0$, $6$, and $3$.
Now we consider the value of x as $0$, the value of y is
$ \Rightarrow 0 = - 6y$
\[ \Rightarrow y = \dfrac{0}{{ - 6}}\]
$ \Rightarrow y = 0$
Now we consider the value of x as $6$, the value of y is
$ \Rightarrow 6 = - 6y$
$ \Rightarrow y = \dfrac{6}{{ - 6}}$
$ \Rightarrow y = - 1$
Now we consider the value of x as $3$, the value of y is
$ \Rightarrow 3 = - 6y$
\[ \Rightarrow y = \dfrac{3}{{ - 6}}\]
\[ \Rightarrow y = \dfrac{{ - 1}}{2}\]
Now we draw a table for these values we have

x	$0$	$6$	$3$
y	$0$	$ - 1$	$ - \dfrac{1}{2}$

The graph plotted for these point is represented below:

Note: There are infinitely many points that satisfy the equation of a given line. 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 points may vary from person to person, but the graph of the straight line remains the same.