Calculating tangent lines

Function #f# is given by the function rule #f(x)= 7\cdot \euler^{x}+8\cdot x#. Let #k# be the tangent line to the graph of #f# at #x=5#.

How do we find the formula for #k#? Drag the steps of the solution into the correct order.

#y = \left ( 7\cdot \euler^5+8 \right ) \cdot x -28\cdot \euler^5#

Calculate #b#, the #y#-intercept of the tangent

Find the #y#-coordinate of the point of tangency

#f(5) = 7\cdot \euler^5+40 #

#f^{\prime}(x) = 7\cdot \euler^{x}+8 #

Calculate the derivative #f^{\prime}(x)#

Determine the slope #a# of the tangent

#7\cdot \euler^5+40 = \left ( 7\cdot \euler^5+8 \right ) \cdot 5 + b#

#a = f^{\prime}(5) = 7\cdot \euler^5+8#

Enter values of #\rv{x,y}# and #a# in #y=a \cdot x+ b#

Give the final formula for #k#

#b = -28\cdot \euler^5#