Final answer:
The equation of the line tangent to the curve y=2x at the point (9,6) is y = 2x - 12.
Step-by-step explanation:
The equation y = 2x represents a straight line with a slope of 2. To find the equation of the line tangent to this curve at the point (9,6), we need to find the slope of the tangent line at that point. Since the slope of the curve y = 2x is always 2, the slope of the tangent line will also be 2.
Using the point-slope form of a line, we can write the equation of the tangent line as follows:
y - y1 = m(x - x1)
where (x1, y1) is the point of tangency and m is the slope of the tangent line.
Plugging in the values (9,6) and m = 2, we get:
y - 6 = 2(x - 9)
Simplifying the equation, we have:
y - 6 = 2x - 18
y = 2x - 12