Question

Determine the missing information in the paragraph proof.

Given: Line PQ contains points (w, v) and (x, z) and line P'Q' contains points (w + a, v + b) and (x + a, z + b). Lines PQ and P'Q' are parallel.

Prove: Parallel lines have the same slope.

On a coordinate plane, 2 lines are shown. Line Q P goes through (w, v) and (x, z). Line Q prime P prime goes through (w + a, v + b) and (x + a, z + b).

Since slope is calculated using the formula m = StartFraction v 2 minus v 1 Over x 2 minus x 1 EndFraction, the slope of both lines is equivalent to ________. It is given that the lines are parallel, and we calculated that the slopes are the same. Therefore, parallel lines have the same slopes.

Answer 1

The slope of both lines is mathematically equivalent to

$Slope=\frac{(z - v)}{ (x - w)}$i

What is the slope of both lines is equivalent to?

Generally, the equation for Slope is  mathematically given as

$S= dy / dx$

Therefore

$Slope of PQ = \frac{(z - v)}{(x - w)}$

$S of P'Q' =\frac{ (z + b - (v + b))}{((x + a) - (w + a))}\\\\S of P'Q' =\frac{ (z - v)}{(x - w)}$

The slopes of both lines are equivalent to

$Slope=\frac{(z - v)}{ (x - w)}$

In conclusion, The slope of both lines is equivalent to

$Slope=\frac{(z - v)}{ (x - w)}$

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