Question

determine the equation of the line that relates the number of pumps to the resulting diameter:
Pumps:
1
2
3
4
5
6
7
8
9
Balloon Diameter:
15
17
20
22
23
25
28
32
34

Answer 1

Are you sure we are concerned with the equation of a line? There doesn't seem to be a constant slope.

Answer 2

thats wjhy i need help, my teacher said that I use y=mx + b form, but it doesnt make a strait line

Answer 3

Is this for Statistics? Are you studying Least Squares? You must have been given some tool to establish your reasonable ability to solve the problem.

Answer 4

it is chemistry lab

Answer 5

Perfect. Then there is absolutely no expectation that you would obtain perfect data. We need to provide a good estimate.

Calculate the slope between each successive pair of points. See how bad it is.

1 15
2 17 2
3 20 3
4 22 2
5 23 1
6 25 2
7 28 3
8 32 4
9 34 2

If you ignore the 1 and 4, it looks like 2.3 might be a good guess - just eyeballing it.
If you average the slope column, you get 2.375. This may be satisfactory. The y-intercept can be somewhat oddly suggested by backing off one more slope from 1 pump. 15 - 2.375 = 12.625, giving Diameter = 2.375(Pumps) + 12.625

You can average successive triplets.

1 15
2 17
3 20 2.5
4 22 2.5
5 23 1.5
6 25 1.5
7 28 2.5
8 32 3.5
9 34 3

The 1st 2.5 is (20-15)/(2-1)

Again, an average gives 2.429. Using the same method for the y-intercept, gives Diameter = 2.429(Pumps) + 12.571

Personally, and you may not have been introduced to this, least-squares is the way to go. This also gives a reasonable estimate of the y-intercept, which is missing from the calculation above.

Diameter = 2.333(Pumps) + 12.333

You may also have some Significant Digit requirements.

It is encouraging that all three linear equations are pretty close to each other.

One word of warning, this model is dubious, at best, for 0 pumps. It should be obvious that the diameter is zero before there is even the fist pump. We just said the diameter will be great than 12 before we even start pumping. It is an unavoidable consequence of the modelling process.

If you graph the three lines against your data, you will see that they all essentially ignore the sag in the middle. This might suggest an experimental design error or measurement error.