Question

Find the equations of the straight lines parallel to the coordinate axes and passing through the point (3, -4).

Answer 1

Hint: The equation of the line parallel to x – axis is y = k and the equation of line parallel to y – axis is x = k, where k is some constant. Use this to solve.

Complete step-by-step answer:
We have been given the question that the straight lines are parallel to the coordinate axes and pass through the point (3, -4).
Now as we know, the equation of line parallel to x – axis is $y = k$.
Now as given in the question that the line passes through the point (3, - 4).
So, putting y = -4, we get the value of k = -4.
Therefore, the equation of line parallel to x axis is $y = - 4$.
Now, the equation of a line parallel to y – axis is $x = k$ .
Again, as given in question the line passes through the point (3, -4).
So, putting x = 3, we get the value of k = 3.
Therefore, the equation of the line parallel to y axis is $x = 3$.
Hence, the equations of the straight lines parallel to the coordinate axes and passing through the point (3, -4) are:
$y = - 4$ and $x = 3$.

Note: Whenever solving such types of questions, write the information given to us in the question. As mentioned in the solution, the straight lines pass through the point (3, -4) and parallel to the coordinate axis. So, we found out the equation of lines parallel to the coordinate axes and then used the condition that these lines pass through the point (3, -4) to find the answer.