Calculating tangent lines

Function $f$ is given by the function rule $f(x)= 3\cdot \euler^{x}+5\cdot x$ . Let $k$ be the tangent line to the graph of $f$ at $x=4$ .

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

Give the final formula for $k$

$a = f^{\prime}(4) = 3\cdot \euler^4+5$

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

$3\cdot \euler^4+20 = \left ( 3\cdot \euler^4+5 \right ) \cdot 4 + b$

$b = -9\cdot \euler^4$

$f(4) = 3\cdot \euler^4+20$

$y = \left ( 3\cdot \euler^4+5 \right ) \cdot x -9\cdot \euler^4$

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

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

$f^{\prime}(x) = 3\cdot \euler^{x}+5$

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

Determine the slope $a$ of the tangent