Prove slope theorems

Line

\overset{\leftrightarrow}{C D}

is the image of

\overset{\leftrightarrow}{A B}

after the translation

(x, y) \to (x + h, y + k)

Complete the proof that the slope of $\overset{\leftrightarrow}{C D}$ ‍ equals the slope of $\overset{\leftrightarrow}{A B}$ ‍.

	Statement	Reason
1	The slope of $\overset{\leftrightarrow}{A B}$ ‍ is $\frac{n - g}{m - f}$ ‍.	Definition of slope
2	$C = (f + h, g + k)$ ‍	Point $C$ ‍ is the image of $A$ ‍ after the translation $(x, y) \to (x + h, y + k)$ ‍.
3	$D = (m + h, n + k)$ ‍	Point $D$ ‍ is the image of $B$ ‍ after the translation $(x, y) \to (x + h, y + k)$ ‍.
4	The slope of $\overset{\leftrightarrow}{C B}$ ‍ is $\frac{(n + k) - (g + k)}{(m + h) - (f + h)}$ ‍.	Definition of slope (2, 3)
5	The slope of $\overset{\leftrightarrow}{C B}$ ‍ is $\frac{n - g}{m - f}$ ‍.	Distribute and collect like terms (4).
6	The slope of $\overset{\leftrightarrow}{C B}$ ‍ equals the slope of $\overset{\leftrightarrow}{A B}$ ‍.	Substitution (1, 5)

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