Calculating tangent lines

Function #f# is given by the function rule #f(x)= 5\cdot \euler^{x}+7\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.

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

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

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

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

Give the final formula for #k#

Determine the slope #a# of the tangent

#f(-5) = 5\cdot \euler^ {- 5 }-35 #

#5\cdot \euler^ {- 5 }-35 = \left ( 5\cdot \euler^ {- 5 }+7 \right ) \cdot (-5) + b#

#b = 30\cdot \euler^ {- 5 }#

#y = \left ( 5\cdot \euler^ {- 5 }+7 \right ) \cdot x + 30\cdot \euler^ {- 5 }#

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

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