Question

5. Find the equation of the line that is perpendicular to the given line and passes through the given point. y = 5x-1; (-1, 1)​

Answer 1

y = -0.2x+ 0.8

Explanation:

If a line is perpendicular to another line then the slope of the line = the negative reciprocal of the other line

Here Line AB has the equation y = 5x - 1. Here slope = 5
This comes from the fact that if a line has the equation y= mx + c then the slope = m and the y intercept = c

If XY is the line perpendicular to AB then its slope = -1/5. Let the y intercept of XY be c

Then equation of line XY is: y = (-1/5)x + c = -0.2x + c (1)

Since it passes through (-1, 1) ie through x = -1, y=1, substitution these values into the above equation (1), we get

1 = (-0.2)(-1) + c or

1 = 0.2 + c or

c = 0.8