Question

How do you graph \[x + y = 1\] by plotting points ?

Answer 1

Hint:A graph of a function f is the set of ordered pairs; the equation of graph is generally represented as \[y = f(x)\], where x and f(x) are real numbers. We substitute the value of x and we determine the value of y and then we mark the points in the graph and we join the points.

Complete step by step answer:
Now consider the given equation \[x + y = 1\], this can be rewritten as \[y = 1 - x\]. Here in this question, we have to plot the graph for the given function. A graph of a function is a set of ordered pairs and it is represented as \[y = f(x)\], where x and f(x) are real numbers. These pairs are in the form of cartesian form and the graph is the two-dimensional graph.First, we have to find the value of y by using the graph equation \[y = 1 - x\]. Let us substitute the value of x has -3, -2, -1, 0, 1, 2, and 3. Now we consider the value of x as -3, the value of y is
\[y = 1 - ( - 3) \\
\Rightarrow y = 1 + 3 \\
\Rightarrow y = 4 \\ \]
Now we consider the value of x as -2, the value of y is
\[y = 1 - ( - 2) \\
\Rightarrow y = 1 + 2 \\
\Rightarrow y = 3 \\ \]
Now we consider the value of x as -1, the value of y is
\[y = 1 - ( - 1) \\
\Rightarrow y = 1 + 1 \\
\Rightarrow y = 2 \\ \]
Now we consider the value of x as 0, the value of y is
\[y = 1 - 0 \\
\Rightarrow y = 1 \\ \]
Now we consider the value of x as 1, the value of y is
\[y = 1 - 1 \\
\Rightarrow y = 0 \\ \]
Now we consider the value of x as 2, the value of y is
\[y = 1 - 2 \\
\Rightarrow y = - 1 \\ \]
Now we consider the value of x as 3, the value of y is
\[y = 1 - 3 \\
\Rightarrow y = - 2 \\ \]
Now we draw a table for these values we have

X	-3	-2	-1	0	1	2	3
y	4	3	2	1	0	-1	-2

The graph plotted for this point is represented below:

Note: The graph is plotted x-axis versus y axis. The graph is two dimensional. By the equation of a graph, we can plot the graph by assuming the value of x. We can’t assume the value of y. because the value of y depends on the value of x. Hence, we have plotted the graph.