Answer:
- y -6 = 2(x -3/2)
- y -3 = x -6
Step-by-step explanation:
The slope of the line is dy/dx. That can be found by differentiation, implicit or otherwise.
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1.
Implicit differentiation:
2y·dy = 24·dx
dy/dx = 24/(2y) = 24/(2·6) = 2 . . . . . at y=6
Then the point-slope equation of the tangent is ...
y -6 = 2(x -3/2)
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2.
Straight differentiation:
2x = 12·dy/dx
dy/dx = x/6 = 6/6 = 1 . . . . . at x=6
Then the point-slope equation of the tangent is ...
y -3 = x -6
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Additional comment
The point-slope equation of a line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
Here, m = dy/dx. (h, k) is the given point of tangency.
