Question

In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?

c−a/b⋅−d/e=−1

c−a/b=d/e

c−a/b⋅d/e=−1

c−a/b=−d/e

Answer 1

B. (c - a)/b = d/e

Explanation:

Slope of upper line:

(c - a)/b

Slope of lower line:

d/e

Parallel lines have equal slopes giving

(c - a)/b = d/e

Answer: B.

Answer 2

`(c-a)/(b)` =
`(d)/(e)`

Parallel lines have equal slopes m

calculate the slope m of each line using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, a) and (x₂, y₂ ) = (b, c )

m =
`(c-a)/(b-0)` =
`(c-a)/(b)`

repeat with

(x₁, y₁ ) = (0, -d ) ) and (x₂, y₂ ) = (e, 0 )

m =
`(0+d)/(e-0)` =
`(d)/(e)`

For the lines to be parallel
`(c-a)/(b)` =
`(d)/(e)` → (b)