Question

What is an equation of the line that passes through the point (4, 1) and is

perpendicular to the line 2x - y = 4?
Answer:

Answer 1

Answer: y₁=-0.5x+3

Explanation:

The equation of the perpendicular line should have an angular coefficient m₁, which is a negative inverse value with respect to the original angular coefficient m

2x-y=4

2x-y+y=4+y

2x=4+y

2x-4=4+y-4

2x-4=y

Thus, y=2x-4

`\displaystyle\\Hence,\\\\m=2\\\\m_1=-(1)/(2)\\\\y_1=-(1)/(2)x+b \\`

Let us find the equation of the perpendicular line using the equation of the line with the angular coefficient and the given point(4,1):

`\displaystyle\\1=-(1)/(2)(4)+b\\\\1=-(4)/(2)+b\\\\\1=-2+b\\\\1+2=-2+b+2\\\\3=b\\\\Thus,\ b=3\\\\Hence, \ y_1=-(1)/(2)x+3 \\\\or\\\\y_1=-0.5x+3`

Answer 2

Explanation:

debatable