Question

How do you write an equation of a line that has no slope and passes through the point $ \left( {5, - 6} \right) $ ?

Answer 1

Hint: In the given problem, we are required to find the equation of a line whose slope is given to us. We can easily find the equation of the line using the slope point form of a straight line. So, we have to substitute the slope and the point given to us in the slope and point form of the line and then simplify the equation of the straight line required.

Complete step-by-step answer:
Given, the slope of line \[ = m = 0\]
Also, Given point on line $ = (5, - 6) $
We know the slope point form of the line, where we can find the equation of a straight line given the slope of the line and the point lying on it. The slope point form of the line can be represented as: $ \left( {y - {y_1}} \right) = m\left( {x - {x_1}} \right) $ where $ \left( {{x_1},{y_1}} \right) $ is the point lying on the line given to us and m is the slope of the required straight line.
Considering $ {x_1} = 5 $ and $ {y_1} = - 6 $ as the point given to us is $ (5, - 6) $
Therefore, required equation of line is as follows:
 $ \left( {y - \left( { - 6} \right)} \right) = 0\left( {x - 5} \right) $
 $ \Rightarrow \left( {y - \left( { - 6} \right)} \right) = 0 $
On opening the brackets and simplifying further, we get,
 $ \Rightarrow \left( {y + 6} \right) = 0 $
 $ \Rightarrow y = - 6 $
Hence, the equation of the straight line is: $ y = - 6 $ .
So, the correct answer is “ $ y = - 6 $ ”.

Note: The given problem requires us to have thorough knowledge of the concepts of coordinate geometry. The equation of the straight line in all the forms must be remembered. The applications of concepts learnt in coordinate geometry are wide ranging.