Question

Find the equation of the line perpendicular to the line x + 2y = 6 and passing through the point (1, 2). Provide full working out please. Thanks :)

Answer 1

y = 2x

Explanation:

the equation of a line in slope- intercept form is

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

given

x + 2y = 6 ( subtract x from both sides )

2y = - x + 6 ( divide through by 2 )

y = -
`(1)/(2)` x + 3 ← 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 (1, 2 ) into the partial equation

2 = 2(1) + c = 2 + c ( subtract 2 from both sides )

0 = c

y = 2x + 0 , that is

y = 2x ← equation of perpendicular line