Question

Draw the graph of the line $x - 3y = 4$ . From the graph, find the ordered pair of points when $y = - 1$ .
$\left( A \right){\text{ }}\left( {7, - 3} \right)$
$\left( B \right){\text{ }}\left( {2,6} \right)$
$\left( C \right){\text{ }}\left( {1, - 1} \right)$
$\left( D \right){\text{ }}\left( {5, - 2} \right)$

Answer 1

Hint:
So we have to find the points which pass through the line $x - 3y = 4$, So for this, we will check the value at $x = 0$ and $y = 0$ . and from this, we will get the two points and joining them will make the equation as mentioned. For the ordered pair we will put the value $y = - 1$ in the equation and then solve for it.

Complete step by step solution:
As we know if the algebraic equation is given to us then from this we can find the points that will pass through it and then sketch the graph.
So we have the equation represented as $x - 3y = 4$ and we have to first find the points to plot the graph.
For $x = 0$ , we have
$ \Rightarrow 0 - 3y = 4$
And on solving, we get
$ \Rightarrow y = \dfrac{{ - 4}}{3}$
Hence, the points will be $\left( {0,\dfrac{{ - 4}}{3}} \right)$
And for $y = 0$ , we have
$ \Rightarrow x - 0 = 4$
And on solving, we get
$ \Rightarrow x = 4$
Hence, the points will be $\left( {4,0} \right)$
Therefore, the graph for the equation $x - 3y = 4$ will be

Now we have to find the ordered pairs and fro this we have to calculate it at $y = - 1$
So we have the equation $x - 3y = 4$ and putting the values of $y$ , we get
$ \Rightarrow x - (3 \times - 1) = 4$
And on solving the above equation, we get
$ \Rightarrow x = 1$
Therefore, the ordered pairs of points will be $(1, - 1)$ .

Hence, the option $\left( c \right)$ is correct.

Note:
From this also we can find the equation by putting these values and on solving we will get back to the equation. We can also use this to recheck the values whether we had got it correct or wrong. And for the graph, we should always note the points on the graph so that it would be easily understandable.