Question

How do you graph \[x \leqslant 6\] on the coordinate plane?

Answer 1

Hint: First we need to draw the graph of the equation\[x = 6\] . We use intercept form to draw the graph. That is we find the coordinate of the given equation lying on the line of x- axis, we can find this by substituting the value of ‘y’ is equal to zero (x-intercept). Similarly we can find the coordinate of the equation lying on the line of y- axis, we can find this by substituting the value of ‘x’ equal to zero (y-intercept). After drawing the graph we can check in which region the inequality satisfies. Here if we draw \[x \leqslant 6\] we will have a parallel line to the y-axis.

Complete step-by-step answer:
Given, \[x \leqslant 6\].
Now consider \[x = 6\]
For \[x = 6\].
Here we don’t have a ‘y’ variable in the given equation.
So ‘x’ will always equal to \[6\], no matter what value we put in for ‘y’, the ‘x’ is always going to be \[6\].
That is,

\[x\]	\[6\]	\[6\]	\[6\]	\[6\]	\[6\]	\[6\]	\[6\]	\[6\]
\[y\]	\[1\]	\[ - 1\]	\[2\]	\[ - 2\]	\[3\]	\[ - 3\]	\[4\]	\[ - 4\]

Let’s plot a graph for this coordinates,
We take scale x-axis= 1 unit = 1 units
                          y-axis= 1 unit = 1 units

For \[x \leqslant 6\], we can see in the graph that we have a straight vertical line that crosses the x axis at \[6\]. The solution is all the coordinate points left to the line \[x = 6\]. If we take coordinate points right to the line the inequality won’t be satisfied.
In the above graph the shaded region is the solution of the given inequality.

Note: We take a point lying on the line \[x = 6\] for the inequality \[x \leqslant 6\]. A graph shows the relation between two variable quantities, it contains two axes perpendicular to each other namely the x-axis and the y-axis. Each variable is measured along one of the axes. In the question, we are given one linear equation containing two variables namely x and y, x is measured along the x-axis and y is measured along the y-axis while tracing the given equations.