Question

How do you graph the line \[y = - x + 8\]?

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:
Here in this question, we have to plot the graph for the given function. A graph of a function is 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 \[y = - x + 8\]. Let we 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
\[
   \Rightarrow y = - ( - 3) + 8 \\
   \Rightarrow y = 3 + 8 \\
   \Rightarrow y = 11 \\
 \]
Now we consider the value of x as -2, the value of y is
\[
   \Rightarrow y = - ( - 2) + 8 \\
   \Rightarrow y = 2 + 8 \\
   \Rightarrow y = 10 \\
 \]
Now we consider the value of x as -1, the value of y is
\[
   \Rightarrow y = - ( - 1) + 8 \\
   \Rightarrow y = 1 + 8 \\
   \Rightarrow y = 9 \\
 \]
Now we consider the value of x as 0, the value of y is
\[
   \Rightarrow y = (0) + 8 \\
   \Rightarrow y = 8 \\
 \]
Now we consider the value of x as 1, the value of y is
\[
   \Rightarrow y = - 1 + 8 \\
   \Rightarrow y = 7 \\
 \]
Now we consider the value of x as 2, the value of y is
\[
   \Rightarrow y = - 2 + 8 \\
   \Rightarrow y = 6 \\
 \]
Now we consider the value of x as 3, the value of y is
\[
  \Rightarrow y = - 3 + 8 \\
   \Rightarrow y = 5 \\
 \]
Now we draw a table for these values we have

X	-3	-2	-1	0	1	2	3
y	11	10	9	8	7	6	5

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.