2 Different answers given the same point and slope

In summary, the equation of the tangent line to the point (1,9) on the curve with a slope of 4 can be found using either the point-slope equation, y-y1 = m(x-x1), or the slope-intercept equation, y = mx+b. After some calculations, it was determined that the correct equation is y = 4x + 5. It was discovered that the mistake made in the process was a simple sign error, a common mistake in mathematical computations.
  • #1
fk378
367
0

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?
 
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  • #2
How did you get each of the answers in section 3 of your post?
 
  • #3
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
 
  • #4
fk378 said:
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?
 
  • #5
Yes, you're right! I really made a silly mistake. Thank you!
 
  • #6
fk378 said:
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...
 

What is the significance of having two different answers given the same point and slope?

The significance of having two different answers given the same point and slope is that it indicates an inconsistency or error in the calculations or data used to determine the slope. This could be due to rounding errors, incorrect data entry, or a flaw in the mathematical formula used to calculate the slope.

How can two different answers be obtained from the same point and slope?

Two different answers can be obtained from the same point and slope if different methods are used to calculate the slope. For example, one method may use a linear regression while another method may use a curve fitting technique. Additionally, errors in data or calculations can also result in different answers.

What should be done in the case of two different answers given the same point and slope?

In the case of two different answers given the same point and slope, it is important to carefully review the data and calculations to determine the source of the discrepancy. If the discrepancy is due to an error, it should be corrected. If the discrepancy is due to different methods used, it may be necessary to select the most appropriate method for the given situation.

Can two different answers given the same point and slope both be correct?

In most cases, it is not possible for two different answers given the same point and slope to both be correct. However, there may be rare cases where different methods or approaches can yield equally valid solutions. It is important to carefully evaluate the data and calculations to determine the accuracy of each answer.

What are some potential sources of error that could result in two different answers given the same point and slope?

Potential sources of error that could result in two different answers given the same point and slope include rounding errors, incorrect data entry, using different mathematical formulas or techniques, and errors in measurements or data collection. It is important to carefully review and verify all data and calculations to minimize these errors.

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