Question

Please help me:( The question is the line y=mx+c passes through the point (3,4) and is perpendicular to the line y+2x=4. Find m and c.

Answer 1

m =
`(1)/(2)` , c =
`(5)/(2)`

Explanation:

the equation of a line in slope- intercept form is

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

given

y + 2x = 4 ( subtract 2x from both sides )

y = - 2x + 4 ← in slope- intercept form

with slope m = - 2

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

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

y =
`(1)/(2)` x + c ← is the partial equation

to find c substitute (3, 4 ) into the partial equation

4 =
`(3)/(2)` + c ⇒ c = 4 -
`(3)/(2)` =
`(5)/(2)`

y =
`(1)/(2)` x +
`(5)/(2)` ← equation of line

with m =
`(1)/(2)` and c =
`(5)/(2)`