Question

Draw the graph of the equation $y = 3x.$Find the value of y, when x =$ - 2$.

Answer 1

Hint: For this type of problems to draw graph of given liner equation we assume or let different value of ‘x’ and then using these values of ‘x’ we find corresponding values of y and then on plotting all these points to obtain graph of given equation and then using given value of x we will find corresponding value of y and hence required solution of the problem.

Complete step-by-step answer:
Given equation is $y = 3x.$
To draw a graph of a given linear equation. We assume or let different values of ‘x’ and then using these values of ‘x’ we find corresponding values of y.
Taking $x = 0$
Therefore, $y = 3(0)$
$ \Rightarrow y = 0$
Hence, we have $\left( {0,0} \right)$
Taking $x = 1$
Therefore, $y = 3\left( 1 \right)$
$ \Rightarrow y = 3$
Hence, we have $\left( {1,3} \right)$
Taking $x = 2$
Therefore, $y = 3\left( 2 \right)$
$ \Rightarrow y = 6$
Hence, we have $\left( {2,6} \right)$
Therefore, from above we have a table of points:

X	0	1	2
Y	0	3	6

Now, we plot all these points in x y plane to obtain graph of equation $y = 3x.$
From the graph we see that for $x = - 2$value of y is$ - 6$.
Hence, coordinate of require point is $\left( { - 2, - 6} \right)$

So, the correct answer is “$\left( { - 2, - 6} \right)$”.

Note: For this type of problem in which a graph of linear equations is required to draw. If the graph of the equation is not coming a straight line then we can say that points taken are wrong as the graph of linear equation is always a straight line. So, if the graph through given points is a straight line and passing through them then it will be a correct sketch for the given linear equation.