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
$\Rightarrow 0=-6y$
$$\Rightarrow y={\displaystyle \frac{0}{-6}}$$
$\Rightarrow y=0$
Now we consider the value of x as $6$, the value of y is
$\Rightarrow 6=-6y$
$\Rightarrow y={\displaystyle \frac{6}{-6}}$
$\Rightarrow y=-1$
Now we consider the value of x as $3$, the value of y is
$\Rightarrow 3=-6y$
$$\Rightarrow y={\displaystyle \frac{3}{-6}}$$
$$\Rightarrow y={\displaystyle \frac{-1}{2}}$$
Now we draw a table for these values we have

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

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.