calculus
posted by art .
f(x)=35x , (1,8) find the slope of the tangent line to the graph of the function at the given point
how do you figure this out?

since your function is a straight line
and it is in the form f(x) = mx + b
the slope anywhere on the line is 5
no work needed here. 
To find the slope of the tangent line you have to take the first derivative of f(x). So f'(x)=5. Or you can also see that from the formula y=mx+b, where m is slope and b is your y intercept, that 5 is the slope. Because the original function is a line, the slope is the same at every point.

To find the slope of the tangent line at a point means to find the derivative of f(x).
f(x) = 3  5x
f' = 0  5
f' = 5
Then, normally, you would plug in the given point, (1, 8), to find the slope.
But since f' = 5 with no variable x, for instance, there is nowhere to plug in the point.
Therefore, the slope is everywhere.