Graph C has a function
[tex]f(x)=2x^3-16x+11[/tex]
Since the line L intersects the graph at the point, A (2, -5)
To find the slope of the line we will differentiate the f(x) and substitute x by 2
[tex]\begin{gathered} f^{\prime}(x)=2(3)x^{3-1}-16x^{1-1}+0 \\ f^{\prime}(x)=6x^2-16 \\ m=6(2)^2-16 \\ m=24-16 \\ m=8 \end{gathered}[/tex]
The slope of the line is 8, substitute it in the form of the linear equation
[tex]\begin{gathered} y=mx+b \\ y=8x+b \end{gathered}[/tex]
To find b substitute x by 2 and y by -5
[tex]\begin{gathered} -5=8(2)+b \\ -5=16+b \end{gathered}[/tex]
Subtract 16 from both sides to find b
[tex]\begin{gathered} -5-16=16-16+b \\ -21=b \end{gathered}[/tex]
Then the equation of the line is
[tex]\begin{gathered} y=8x+(-21) \\ y=8x-21 \end{gathered}[/tex]
