Question

How do you graph $ y = 1.5x $ ?

Answer 1

Hint: Here we have to plot a graph. In this given equation by giving the values to the x like 0, 1, 2, 3, … simultaneously we get the values of y with respect to the x value. after getting the x and y values, write the coordinates of the given equation in the form of (x,y), by using the coordinates to construct the required graph of the given equation.

Complete step-by-step answer:
Given equation in the form of linear equation in the form of two variables x and y
Consider the equation $ y = 1.5x $
Now, by giving the x values 0, 1, 2, 3, … to the above equation simultaneously we get the values of y
When we substitute the value of x=0
Then $ \Rightarrow \,\,y = 1.5\left( 0 \right) $
 $ \therefore \,\,\,y = 0 $
Therefore, coordinate $ \left( {x,y} \right) = \left( {0,0} \right) $
When we substitute the value of x=2
 $ \Rightarrow \,y = 1.5\left( 2 \right) $
 $ \therefore \,\,\,y = 3 $
 Therefore, coordinate $ \left( {x,y} \right) = \left( {2,3} \right) $
When we substitute the value of x=4
 $ \Rightarrow \,y = 1.5\left( 4 \right) $
 $ \therefore \,\,\,y = 6 $
 Therefore, coordinate $ \left( {x,y} \right) = \left( {4,6} \right) $
When we substitute the value of x=6
 $ \Rightarrow \,y = 1.5\left( 6 \right) $
 $ \therefore \,\,\,y = 9 $
 Therefore, coordinate $ \left( {x,y} \right) = \left( {6,9} \right) $
When we substitute the value of x=8
 $ \Rightarrow \,y = 1.5\left( 8 \right) $
 $ \therefore \,\,\,y = 12 $
 Therefore, coordinate $ \left( {x,y} \right) = \left( {8,12} \right) $
And so on …
Hence by substituting the value of x we have determined some of the values or points we use to plot the graph.
The coordinates can be written in table as :

$ x $	$ 0 $	$ 2 $	$ 4 $	$ 6 $	$ 8 $
$ y $	$ 0 $	$ 3 $	$ 6 $	$ 9 $	$ 12 $
$ \left( {x,y} \right) $	$ \left( {0,0} \right) $	$ \left( {2,3} \right) $	$ \left( {4,6} \right) $	$ \left( {6,9} \right) $	$ \left( {8,12} \right) $

Now, the graph of the given linear equation $ y = 1.5x $ by using the above table as follows:

Note: The graph is plotted x-axis versus y axis. The graph is two dimensional. By the given equation write it for y and consider it as a graph equation. 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.