Let f(x)= 8x + 3 − 7e^x

Question

Then the equation of the tangent line to the graph of  at the point  is given by  for

m=

b=

Answer 1

Lola,

The slope of the tangent line is given by f'(0).

The y-intercept is where the tangent line crosses the y-axis. It is given to you in the problem.

Answer 2

Since the derivative is the slope[m] of the tangent line, you first take the derivative of the entire equation to get f'(x) = 8-7e^x. Then you put in 0 for x since that's the x-coordinate for the point in the tangent line that we're referring to. You get m=1 as a result. Then you put m and the coordinates of the point back into y = mx + b in order to get -4 = (1)(0) + b. Then you just evaluate the equation to get b = -4.