Question

Find the equation of the line the (2, 6) and is perpendicular to the equation y = 2x + 8

Answer 1

Answer: y= -1/2x+7

Step-by-step explanation: use the point slope form and use the -1/2x like the slope because the perpendicular lines are negative reciprocals.

Answer 2

y = -0.5x + 7

Explanation:

Equation of a Line is y = mx + c

where m is the slope and c is the y-intercept

Given two lines are Perpendicular

Then
`m_(1) m_(2) =-1`

So we given Line whose Equation is y = 2x +8

Then
`m_(1) =2` (Coefficient of x)

Since the Line we want is Perpendicular to that line

Then
`m_(1) m_(2) =-1` ,
`2m_(2) =-1 , m_(2) =(-1)/(2)`

So the Equation of the required Line is y = -0.5x +c

Since the Line passes through (2 , 6) , Then y = 6 when x = 2

By substitution , 6 = -0.5*2 + c , 6 = -1 + c

Then c = 6+1 =7

Then the Equation will be y = -0.5x + 7