Question

How do you graph the inequality $x < \- 4$ on the coordinate plane ?

Answer 1

First we need to draw the graph of the equation$x = - 4$ . 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 $x < \- 4$ we will have a parallel line to the y-axis.

Complete step by step answer:
Given, $x < \- 4$. Now consider $x = - 4$.
For $x = - 4$.
Here we don’t have a ‘y’ variable in the given equation. So ‘x’ will always equal to $- 4$, no matter what value we put in for ‘y’, the ‘x’ is always going to be $- 4$. That is,

$x$	$- 4$	$- 4$	$- 4$	$- 4$	$- 4$	$- 4$	$- 4$	$- 4$
$y$	$1$	$- 1$	$2$	$- 2$	$3$	$- 3$	$4$	$- 4$

Let’s plot a graph for these coordinates. We take scale x-axis= 1 unit = 1 units and y-axis= 1 unit = 1 units.

For $x < \- 4$, we can see in the graph that we have a straight vertical line that crosses the x axis at $- 4$. The solution is all the coordinate points left to the line $x = - 4$. 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 don’t take points lying on the line $x = - 4$ for the inequality $x < \- 4$. 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.