Question

Write the equation of a line that is perpendicular to the line y = 1/2x + 1 and goes through 6 on the x axis​

Answer 1

SHORTCUT METHOD :

GIVEN EQUATION IS y = 1/2x + 1

• This method teach us in order to write this equation in perpendicular form we will change the coefficient of Y axis in to X axis and X axis into Y axis by a negative of sign WITH ONE of them and rePlace constant term as K

NOW PERPENDICULAR EQUATION CAN BE WRITTEN AS

y = -2x + k

Since the line passes through the point (6,0) on the x-axis, we can substitute these values into the equation to solve for k:

• 0 = -2(6) + k
• 0 = -12 + k
• k = 12
• Therefore, the equation of the line that is perpendicular to y = 1/2x + 1 and passes through the point (6,0) is

y = -2x + 12.

Answer 2

y = - 2x + 12

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y =
`(1)/(2)` x + 1 ← is in slope- intercept form

with slope m =
`(1)/(2)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((1)/(2) )` = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (6, 0 ) , the point it crosses on the x- axis into the partial equation.

0 = - 2(6) + c = - 12 + c ( add 12 to both sides )

12 = c

y = - 2x + 12 ← equation of perpendicular line