Answer:
The perpendicular line is
x = 4
Step-by-step explanation:
Parameters:
Line: y = -3
Point: (4, -6)
If two lines are perpendicular, then the slope of one is the negative reciprocal of the slope of the other.
The slope of the line:
y = -3
is zero
The negative reciprocal of 0 is -1/0, which is undefined.
Hence, we say the perpendicular line is:
x = k
Where k is any real number.
Examples of the perpendicular lines are:
x = 1, x = 2, x = 1/2, etc
Now, given the point (4, -6), we put x = 4 in the line x = k, so that
k = 4.
Therefore, the required perpendicular line is:
x = 4
Graph:
The graph of y = -3 is a horizontal straight line that cuts through -3 on the y-axis
The graph of x = 4 is a vertical straight line that cuts through 4 on the y-axis.