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

$\frac{c-a}{b}$ = $\frac{d}{e}$

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 = $\frac{c-a}{b-0}$ = $\frac{c-a}{b}$

repeat with

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

m = $\frac{0+d}{e-0}$ = $\frac{d}{e}$

For the lines to be parallel $\frac{c-a}{b}$ = $\frac{d}{e}$ → (b)

Answer 2

Answer:

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

Step-by-step 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.