Question

How do you graph the line $ y = \dfrac{2}{3}x - 5 $ ?

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\left( x \right) $ , 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 solution:
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\left( x \right) $ , 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 = \dfrac{2}{3}x - 5 $ . Let we substitute the value of x has $ 0 $ , $ 3 $ , $ 6 $ and $ 9 $ .
Now we consider the value of x as $ 0 $ , the value of y is
  $ \Rightarrow y = \dfrac{2}{3}x - 5 $
  $ \Rightarrow y = \dfrac{2}{3}\left( 0 \right) - 5 $
  $ \Rightarrow y = - 5 $
Now we consider the value of x as $ 3 $ , the value of y is
  $ \Rightarrow y = \dfrac{2}{3}x - 5 $
  $ \Rightarrow y = \dfrac{2}{3}\left( 3 \right) - 5 $
  $ \Rightarrow y = - 3 $
Now we consider the value of x as $ 6 $ , the value of y is
  $ \Rightarrow y = \dfrac{2}{3}x - 5 $
  $ \Rightarrow y = \dfrac{2}{3}\left( 6 \right) - 5 $
  $ \Rightarrow y = - 1 $
Now we consider the value of x as $ 9 $ , the value of y is
  $ \Rightarrow y = \dfrac{2}{3}x - 5 $
  $ \Rightarrow y = \dfrac{2}{3}x - 5 $
  $ \Rightarrow y = 1 $
Now we draw a table for these values we have

x	$ 0 $	$ 6 $	$ 3 $	$ 9 $
y	$ - 5 $	$ - 1 $	$ - 3 $	$ 1 $

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.