Question

How do you graph \[y=x-2\] using a table of values?

Answer 1

Hint: From the question we have been asked to find the graph of a function with the help of table of values. To solve this question we will find the points on the graph using the substitution method. We will substitute a value for x and find the corresponding value of the y from the function \[y=x-2\]. From those points which we found using the substitution method using them we will plot the graph.

Complete step by step answer:
Firstly, we will find the points on the graph by substituting a x value in the given function which is \[y=x-2\].
So, now we will substitute \[x=-2\] in the function and find the value of y. so, we get,
\[\Rightarrow y=x-2\]
\[\Rightarrow y=-2-2\]
\[\Rightarrow y=-4\]
So, we got the point as \[(-2,-4)\].
Similarly we will find another set of points so that it helps us to graph easily.
So, now we will substitute the value of x as \[x=-1\]. So, we get,
\[\Rightarrow y=x-2\]
\[\Rightarrow y=-1-2\]
\[\Rightarrow y=-3\]
So, we got the point as \[(-1,-3)\].
Now, we will substitute the value of x as \[x=0\]. So, we get,
\[\Rightarrow y=x-2\]
\[\Rightarrow y=-2\]
So, we got the corresponding point as \[(0,-2)\].
Now, we will substitute the value of x as \[x=1\]. So, we get,
\[\Rightarrow y=x-2\]
\[\Rightarrow y=1-2\]
\[\Rightarrow y=-1\]
So, we got the point as \[(1,-1)\].
We will find one more point and with the help of these points we will draw the graph.
Now, we will substitute the value of x as \[x=2\]. So, we get,
\[\Rightarrow y=x-2\]
\[\Rightarrow y=2-2\]
\[\Rightarrow y=0\]
The table of these values will be as follows.

x-value	y-value
-2	-4
-1	-3
0	-2
1	-1
2	0

Therefore, the graph of the given question will be as follows.

Note: Students should not do any calculation mistakes. Students must have good knowledge in this substitution method and finding the points on a graph using a given function. Students should not make mistakes in taking the point wrong for example in the first case if we take the point as \[(-4,-2)\] instead of \[(-2,-4)\] our solution will be wrong.