Question

Draw the graph of the following linear in two variables \[y = 3x\].

Answer 1

Hint: First we find which of the two variables is dependent on the other variable. Substitute the values of independent variables one by one and write the respective values of dependent variables. Write the values in terms of Cartesian coordinates and plot on the graph.

Complete step-by-step answer: We are given a linear equation in two variables x and y.
We know that the graph of a linear equation in two variables is always a line. So the given linear equation\[y = 3x\] will be represented by a line on the graph.
Now we can see in the given equation we have y as multiple of x. So we can say x is the independent variable and y attains any value depending on the value of x, so y is the dependent variable.
We substitute values of x and find the values of y.
Put \[x = 0\] in equation \[y = 3x\]
\[ \Rightarrow y = 3 \times 0\]
\[ \Rightarrow y = 0\]
So, the point becomes \[(0,0)\]
Put \[x = 1\] in equation \[y = 3x\]
\[ \Rightarrow y = 3 \times 1\]
\[ \Rightarrow y = 3\]
So, the point becomes \[(1,3)\]
Put \[x = - 1\] in equation \[y = 3x\]
\[ \Rightarrow y = 3 \times ( - 1)\]
\[ \Rightarrow y = - 3\]
So, the point becomes \[( - 1, - 3)\]
Let us name the points \[A(0,0),B(1,3)\] and \[C( - 1, - 3)\]
Now we draw Cartesian plane i.e. XY plane and plot the points A, B and C

Now join the three points forming a straight line.

So, the graph of the linear equation is a line.

Note: Students can get confused while plotting the points on the graph if they don’t write the value of x and y in terms of Cartesian coordinates which clarifies that first element is for x-axis and second element is for y-axis. Also while plotting the graph always try to join the points using straight lines, don’t make curvy lines.
* Independent variable is the variable that can take any value and is not affected by any other variable.
* Dependent variable is the variable that is dependent on the independent variable. So any change in the value of the independent variable will bring a change in dependent variable.
* Any point on the Cartesian plane is called Cartesian coordinate and is written as \[(a,b)\] where a is the distance of point from origin on x-axis and b is the distance of point from origin on y-axis.