Question

I need help solving this problem.

Answer 1

y =
`(1)/(4)` x -
`(9)/(2)`

Explanation:

The equation of a line in slope- intercept form is

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

y = - 4x + 38 is in this form with slope m = - 4

The line ST is perpendicular to line RS ( angles in a square are 90° )

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-4)` =
`(1)/(4)`

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

To find c substitute (2, - 4) into the partial equation

- 4 =
`(1)/(2)` + c ⇒ c = - 4 -
`(1)/(2)` = -
`(9)/(2)`

y =
`(1)/(4)` x -
`(9)/(2)` ← equation of ST