What line is perpendicular to $y = - 3$ and passes through point $\left( {4, - 6} \right)$?

Hint: We are supposed to find the equation of line that is perpendicular to$y = - 3$. Here, $y = - 3$ is a horizontal line. So the line perpendicular to this equation must be a vertical line. Also it must be passing through point $\left( {4, - 6} \right)$. So, let us look at the graphs below and find out the equation.

Complete step by step solution:
In this question, we are given an equation of line $y = - 3$ and we are supposed to find another equation of line that is perpendicular to this line and also passes through the point $\left( {4, - 6} \right)$.
Now, first of all let us draw the graph for $y = - 3$.

Here, we can see that the equation $y = - 3$ is of a straight horizontal line. So, the line that will be perpendicular to this equation must be a vertical line.
And also, it is given that the vertical line should be passing through point $\left( {4, - 6} \right)$.
So therefore, $x = 4$ will be perpendicular to the given line $y = - 3$ and will be passing through the point $\left( {4, - 6} \right)$.
Let us draw the graph for $x = 4$ and see whether our answer is correct or not.

Here, in this graph we can see that the line $x = 4$ is perpendicular to the line $y = - 3$ and it is passing through the x coordinate 4.
Hence, our answer is correct.

Note:
> Note that if you are asked to find a line parallel to the given line that line must be a horizontal line and if the given line is also horizontal line, then it must not intersect the given line.
> Also, remember that the product of slopes of two perpendicular lines is always equal to $ - 1$.