Question

Can anyone help me pls I would appreciate it

Answer 1

t = b + n

Explanation:

for the 2 lines to be parallel then their slopes must be equal

calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (x₁, a + n ) and (x₂, y₂ ) = (x₂, t ) ← 2 points on line k

m =
`(t-(a+n))/(x_(2)-x_(1) )` =
`(t-a-n)/(x_(2)-x_(1) )`

repeat with

(x₁, y₁ ) = (x₁, a ) and (x₂, y₂ ) = (x₂, b ) ← 2 points on line j

m =
`(b-a)/(x_(2)-x_(1) )`

equating the 2 slopes gives

`(t-a-n)/(x_(2)-x_(1) )` =
`(b-a)/(x_(2)-x_(1) )`

since the denominators are the same on both sides, then equate the numerators

t - a - n = b - a ( add a to both sides )

t - n = b ( add n to both sides )

t = b + n