Question

Find the equation of the line through the point $\left( {6, - 1} \right)$ i.e, perpendicular to the y-axis.

Answer 1

Hint : In this problem, we have given the coordinates $\left( {6, - 1} \right)$ of the line and the line is perpendicular to y-axis, or we can say that the line is horizontal to x-axis and when the line is horizontal, it means that it doesn’t touch any point on x-axis and hence, the equation of the line becomes the y-intercept.

Complete step by step solution:
We have given that the line is perpendicular to the y-axis and hence, it is horizontal at x-axis and the equation of a line runs through $\left( {6, - 1} \right)$ . And we know that the equation of any horizontal line is the y-intercept. Here, the line runs through the point
$\left( {x,y} \right) = \left( {6, - 1} \right)$
From this, the value of y is $- 1$ and the line is horizontal to x-axis and then, the value of y must be the y-intercept, then the equation becomes $y = - 1$ and if the line passes through some other point on y-axis, then the value of the equation will change, accordingly.
So, the correct answer is “ $y = - 1$ ”.

Note : The equation of a straight line is $y = mx + c$ , where m is the slope, $\left( {x,y} \right)$ is the point given on the line and c is the y-intercept.
Note: In this case, it doesn’t matter, what the x coordinate is, as the line is perpendicular to y-axis but if in the question, it is given that it is horizontal to y-axis, or we can say that the line is perpendicular to x-axis then the equation becomes for the value of x and in this case the equation will become $x = - 6$ . If the line passes through some other point on x-axis, then the value of the equation will change.