Question

What is the equation of the line that passes through the given point and is perpendicular to the given line?

Point: (1,1)
Line: y=1/5x+4/5

1. y=−5x+6

2. y=−5x+4/5

3. y=1/5x−1/5

4. y=−5x−5/4

Answer 1

Answer:
`y=-5x+6`

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. Since the slope of the given line is
`1/5`, the slope of the line we need to find is
`-5`.

Using point-slope form, the equation is
`y-1=-5(x-1)`.

Converting to slope-intercept form:

`y-1=-5(x-1)\\\\y-1=-5x+5\\\\y=-5x+6`