Question: The graph of \[y = |x|\] consists of pair of straight lines lying 1) To the left of y-axis 2) Ab...

Question

The graph of $y = |x|$ consists of pair of straight lines lying

To the left of y-axis
Above x-axis
Below y-axis
To the right of y-axis

Answer 1

Solution

We are given an equation $y = |x|$ and we need to find the graph of this equation. First, we will remove the mod sign of x, so we get two values of y. Then, we will substitute the values of x to get the values of y. And then, these values are used to plot the graph and thus, we get our final output.
Graphing is always about actually plotting the points to obtain a representative diagram.

Complete answer:
Given that, the equation $y = |x|$ .
We know that,
The graph of the equation y = a, is always a straight line parallel to x-axis.
We need to find the graph of the given equation.
First we will remove the mod sign of x, then
$y = x,{\text{ }}x > 0$ and $y = - x,{\text{ }}x < 0$
Let's substitute the value of x to get the value of y and then we will plot in the graph.
For, the equation $y = x$
When $x = 0,{\text{ }}y = 0$
$x = 1,{\text{ }}y = 1$
$x = 2,{\text{ }}y = 2$
$x = 3,{\text{ }}y = 3$ and so on…
Thus, we get positive values of y, when $x > 0$ .
Next, for the equation $y = - x$
When $x = - 1,{\text{ }}y = - 1$
$x = - 2,{\text{ }}y = - 2$
$x = - 3,{\text{ }}y = - 3$ and so on…
Thus, we get negative values of y, when $x < 0$ .
Now, we will plot these points on the graph as below:

So, we get a graph which consists of a pair of straight lines lying above the x-axis.
Hence, for the given equation $y = |x|$ we get a graph which consists of a pair of straight lines lying above the x-axis.

Note:
Linear equations, also known as first-order degree equations, where the highest power of the variable is one. When an equation has one variable, it is known as linear equations in one variable. When it has two variables, then it is called a linear equation with two variables. Every linear equation in two variables can be represented geometrically as a straight line in a coordinate plane. Points on the line are the solution of the equation. This is why equations with degree one are called linear equations.