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Answer:
y -k = m(x -h)
Explanation:
To translate a function right by h units, replace x with (x -h).
To translate a function up by k units, replace y with (y -k).
The translated function is ...
y -k = m(x -h)
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Additional comment
You may recognize this as the "point-slope" form of the equation of a line. The "parent function" is the line through the origin with slope m:
y = mx
The translation above makes it be a line through (h, k) with slope m.