Question

Write the equation in slope intercept form for a line perpendicular to 2y-10x=6 and passing through the point (15,-1).

Answer 1

y = -
`(1)/(5)` x + 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 the line with equation

2y - 10x = 6 ( add 10x to both sides )

2y = 10x + 6 ( divide through by 2 )

y = 5x + 3 ← in slope- intercept form

with slope m = 5

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

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

y = -
`(1)/(5)` x + c ← is the partial equation of the perpendicular line

to find c, substitute the point (15, - 1 ) into the partial equation

- 1 = -
`(1)/(5)` (15) + c = - 3 + c ( add 3 to both sides )

2 = c

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