Question

10. Choose the correct answer. perpendicular to 'y=5/2x-6' and has the point (5,-7)

a. y= 2/5x-9

b. y= -5/2x+14

c. y= 5/2x-39

d. y= -2/5x-5​

Answer 1

d

Explanation:

The equation of a line in slope- intercept form is

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

y =
`(5)/(2)` x - 6 ← is in slope- intercept form

with slope m =
`(5)/(2)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((5)/(2) )` = -
`(2)/(5)` , then

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

To find c substitute (5, - 7) into the partial equation

- 7 = - 2 + c ⇒ c = - 7 + 2 = - 5

y = -
`(2)/(5)` x - 5 ← equation of perpendicular line → d