2 Different answers given the same point and slope

[fk378]

Homework Statement

Given the point (1,9) on a curve, and the slope = 4, what is the equation of the tangent line to the point?

Homework Equations

#1) y-y1 = m (x-x1)
or
#2) y = mx+b

The Attempt at a Solution

Using equation #1, I got y = 4x-3
Using equation #2, I got y = 4x+5

What am I doing wrong here?

 

[EnumaElish]

How did you get each of the answers in section 3 of your post?

 

[fk378]

Here are my computations:

1) y-y1 = m(x-x1):
y-1 = 4 (x-1)
y = 4x - 4 + 1
y = 4x -32) y = mx +b
9 = 4 (1) + b
5 = b
therefore, y = 4x + 5

 

[dynamicsolo]

Here are my computations:

1) y-y1 = m(x-x1):
y-1 = 4 (x-1)
y = 4x - 4 + 1
y = 4x -3

In this point-slope equation, isn't y1 = 9?

 

[fk378]

Yes, you're right! I really made a silly mistake. Thank you!

 

[dynamicsolo]

Yes, you're right! I really made a silly mistake. Thank you!

From my long years of having taken exams, graded exams, and helped students with post-mortems on exams, I can tell you that the number 1 type of mistake people make is *sign* errors and the number 2 type is *copying* errors. Everyone, including the professionals, makes them (occasionally, these errors even get into published journal papers!). Knowing this won't keep you from ever making mistakes again, but it does help you keep alert for where things may have gone wrong...