Question

How do you graph the line y = 4x – 2?

Answer 1

Hint: We will first put x = 0 and then put x = 1 to find different values of y for different x and thus we have two points on the given line. Now, joining those with the help of line segments, we have the required line.

Complete step-by-step solution:
We are given that we are required to draw the graph of y = 4x – 2.
Now, we will, first of all find two points which exist on the line y = 4x – 2.
Let us put x = 0 in the given equation y = 4x – 2, we will then obtain the following equation with us:-
$ \Rightarrow $y = 4 (0) – 2
Simplifying the calculations in the right hand side, we will then obtain the following equation as:-
$ \Rightarrow $y = 0 – 2
Simplifying the calculations in the right hand side further, we will then obtain the following equation as:-
$ \Rightarrow $y = – 2
Now, let us put x = 1 in the given equation y = 4x – 2, we will then obtain the following equation as:-
$ \Rightarrow $y = 4 (1) – 2
Simplifying the calculations in the right hand side, we will then obtain the following equation as:-
$ \Rightarrow $y = 4 – 2
Simplifying the calculations in the right hand side further, we will then obtain the following equation as:-
$ \Rightarrow $y = 2
Thus, we have the following table with us:-

x	0	1
y	-2	2

Now, plotting these points and joining those lines, we will have the following graph as:-

Note: The students must note the fact that we have just found two points which exist on the line because through specific two points, only one unique line passes through it. Thus, only two points are enough to draw the equation of the line.
The students must also note the following fact used by us in the solution mentioned above:-
For any a in real numbers a times 0 is always equal to 0.