Calculating tangent lines

Function #f# is given by the function rule #f(x)= 10\cdot \euler^{x}+7\cdot x#. Let #k# be the tangent line to the graph of #f# at #x=-1#.

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

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

#y = \left ( 10\cdot \euler^ {- 1 }+7 \right ) \cdot x + 20\cdot \euler^ {- 1 }#

#f^{\prime}(x) = 10\cdot \euler^{x}+7 #

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

#10\cdot \euler^ {- 1 }-7 = \left ( 10\cdot \euler^ {- 1 }+7 \right ) \cdot (-1) + b#

#a = f^{\prime}(-1) = 10\cdot \euler^ {- 1 }+7#

Give the final formula for #k#

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

#b = 20\cdot \euler^ {- 1 }#

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

Determine the slope #a# of the tangent

#f(-1) = 10\cdot \euler^ {- 1 }-7 #