Question

How do you graph the line $y = - 5x + 2$?

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 $y = - 5x + 2$. 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 = - 5( - 3) + 2 \\
   \Rightarrow y = + 15 + 2 \\
   \Rightarrow y = 17 \\
 $
Now we consider the value of x as -2, the value of y is
$
   \Rightarrow y = - 5( - 2) + 2 \\
   \Rightarrow y = + 10 + 2 \\
   \Rightarrow y = 12 \\
 $
Now we consider the value of x as -1, the value of y is
$
   \Rightarrow y = - 5( - 1) + 2 \\
   \Rightarrow y = + 5 + 2 \\
   \Rightarrow y = 7 \\
 $
Now we consider the value of x as 0, the value of y is
$
   \Rightarrow y = - 5(0) + 2 \\
   \Rightarrow y = 0 + 2 \\
   \Rightarrow y = 2 \\
 $
Now we consider the value of x as 1, the value of y is
$
   \Rightarrow y = - 5(1) + 2 \\
   \Rightarrow y = - 5 + 2 \\
   \Rightarrow y = - 3 \\
 $
Now we consider the value of x as 2, the value of y is
$
   \Rightarrow y = - 5(2) + 2 \\
   \Rightarrow y = - 10 + 2 \\
   \Rightarrow y = - 8 \\
 $
Now we consider the value of x as 3, the value of y is
$
   \Rightarrow y = - 5(3) + 2 \\
   \Rightarrow y = - 15 + 2 \\
   \Rightarrow y = 13 \\
 $
Now we draw a table for these values we have

X	-3	-2	-1	0	1	2	3
y	17	12	7	2	-3	-8	-13

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.