Question

How do you graph $$x-y=1$$ by plotting points?

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 $$x-y=1$$. From those points which we found using the substitution method using them we will plot the graph.

Complete step by step solution:
Firstly, we will find the points on the graph by substituting x value in the given function which is $$x-y=1$$.
So, now we will substitute $$x=1$$ in the function and find the value of y. so, we get,
$$\Rightarrow x-y=1$$
$$\Rightarrow 1-y=1$$
$$\Rightarrow y=0$$
So, we got the point as $$(1,0)$$.
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 $$x=0$$. So, we get,
$$\Rightarrow x-y=1$$
$$\Rightarrow 0-y=1$$
$$\Rightarrow y=-1$$
So, we got the point as $$(0,-1)$$.
Now, we will substitute the value of x as $$x=2$$. So, we get,
$$\Rightarrow x-y=1$$
$$\Rightarrow 2-y=1$$
$$\Rightarrow y=1$$
So, we got the corresponding point as $$(2,1)$$.
Now, we will substitute the value of x as $$x=3$$. So, we get,
$$\Rightarrow x-y=1$$
$$\Rightarrow 3-y=1$$
$$\Rightarrow y=2$$
So, we got the point as $$(3,2)$$.
So, the points we plotted are $$(1,0)$$, $$(0,-1)$$,$$(2,1)$$,$$(3,2)$$.
We will take the help of these points and we will draw the graph.
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 $$(0,1)$$ instead of $$(1,0)$$ our solution will be wrong.