Question

How do you graph $y - 2x = 0$ by plotting points?

Answer 1

Hint: We can draw a graph by taking many points that satisfy the equation. Here we will take five points that satisfy the equation $y - 2x = 0$ and then plot them in the graph paper. In the end, we will join the points and will get the graph.

Complete step-by-step solution:
At first, we will take the equation $y - 2x = 0$ .
We can write it as $y = 2x$ .
Now we will choose five values for $y$ and then w.r.t. the values of $y$ we will find the values of $x$ .
Let us take the values $2$ , $10$ , $0$ , $ - 4$ and $ - 10$ of $y$ .
When $y = 2$ ;
From the given equation;
$2x = 2$
$ \Rightarrow x = 1$
When $y = 10$ ;
From the given equation;
$2x = 10$
$ \Rightarrow x = 5$
When $y = 0$ ;
From the given equation;
$2x = 0$
$ \Rightarrow x = 0$
When $y = - 4$ ;
From the given equation;
$2x = - 4$
$ \Rightarrow x = - 2$
When $y = - 10$ ;
From the given equation;
$2x = - 10$
$ \Rightarrow x = - 5$
So, we get the points to plot and the points are $(1,2)$ , $(5,10)$ , $(0,0)$ , $( - 2, - 4)$ and $( - 5, - 10)$ .
Now to plot this point we have to take the basic coordinate system such that $(0,0)$ as O and two perpendicular lines XOX’ and YOY’ passing through the point origin O.
Now we will plot these points and will get this graph;

Clearly, this is a graph of the given equation $y - 2x = 0$ and the equation is of a straight line passing through the origin $(0,0)$ .

Note: Students try to take a minimum of three points to plot any graphs. As much as you have taken the points your graph will be appropriate more. In the case of plotting a curve, the process is not the same as for the straight-line cause it may happen in between or except the three points the curve changed its path. Do not forget to mention the axes and the origin.