Question

How do you graph $y = 2x + 1$ using a table?

Answer 1

Hint:A graph is a visual diagram used to represent equations or functions or any statistical information. To plot a graph for an equation, we must know the coordinates of the graph. Coordinates of the graph can be found by assuming certain values for either $x$ or $y$ in the given equation and then finding out the value of another variable with the help of it.

Complete step by step solution:
The given equation for which the graph shall be plotted is $y = 2x + 1$.
Firstly let us take $x = 0$, so
 $
  y = 2 \times 0 + 1 \\
   \Rightarrow y = 1 \\
 $
When $x = 0$, $y = 1$.
Secondly let us take $x = 1$, so
$
  y = 2 \times 1 + 1 \\
   \Rightarrow y = 2 + 1 \\
   \Rightarrow y = 3 \\
 $
When $x = 1$, $y = 3$.
Lastly let us take $x = - 1$, so
$
  y = 2 \times - 1 + 1 \\
   \Rightarrow y = - 2 + 1 \\
   \Rightarrow y = - 1 \\
 $
When $x = - 1$, $y = - 1$.
So we obtain a table given below:

$x$	$0$	$1$	$ - 1$
$y$	$1$	$3$	$ - 1$

With the help of this table, we can locate the coordinates $(x,y)$ given and hence plot a graph given below:

Note: Coordinates are a set of values that show an exact position. On graphs, it is usually a pair of numbers. The first number shows the distance along the $x$ axis or the horizontal axis and the second number shows the distance along the $y$ axis or the vertical axis. Also, coordinates can have three numbers where the third number is used to denote the distance along the $z$ axis. Such coordinates are used to locate points in 3d or space.