Question

Help Solving and can you go in to detail how you solved it

Answer 1

t = b + n

Explanation:

• Parallel lines have equal slopes

calculate the slopes of lines j and k using the slope formula and then equate them

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

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

substitute these values into the formula for m

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

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

substitute these values into the formula for m

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

equate the 2 values for slope m

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

equate the numerators

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

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

t = b + n

For lines j and k to be parallel , then t = b + n