Solve for the equation using y' as the slope and the given point (2, 4).

Question

Solve for the equation using y' as the slope and the given point (2, 4).

y - y1 = m( x - x1 )

Y - ? = ? ( x - 2 )

y - ? = ? x - 16

Therefore, the equation of the line tangent to the graph is ?

Answer 1

This looks like one of those webassign problems.

Since we are dealing with a tangent line, the magnitude of y' at the intersection point shows up as the coefficient m in the tangent line.

The intersection point is given by (x₁,y₁) = (2,4)

y - 4 = m(x-2)

y - 4 = mx - 2m = mx -16

From this step, we see -2m =-16

so m = -16/-2 = 8.

Thus the equation is

y - 4 = 8x -16

or y = 8x - 12

Answer 2

y - 4 = 8(x - 2) or y = 8x - 12