Question

What is an equation of the tangent line at x = 5, assuming that y(5) = 4 and y'(5) = 2?

Answer 1

We have all the information we need to fill in the blanks. No real math is needed.
Recall the equation of a tangent line is a line and therefore can be written as
y-y1=m(x-x1)
Where m is the slope at x=x1 and (x1,y1) is a point on the curve

Answer 2

So it would be the points (5,4) (5,2)?

Answer 3

I only see on point on y
that is (5,4)

Answer 4

The other equation you wrote is giving you the slope at x=5

Answer 5

That little ' denotes derivative (slope)

Answer 6

Oh! so the slope is 2? so it would be y-4=(2(x-5)

Answer 7

looks good

Answer 8

wow thank you so much for your help!!