Graphing these points and finding the slope form of it?
So I have a table with the values: (1, 9.5),(2, 12.5),(3, 17),(4, 21),(5, 26)... and It's asking for the slope form of the line(y=mx+b), but I can't find the slope value of it considering that it doesn't fallow any proportion. How I'm supposed to calculate it?
Thank you!
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answers:
llaffer say: This problem wants you to find an approximate line that goes near the points to show any possible trending.

I found this method (Least Square Method) linked below. The steps are:

Find the mean of x values and the mean of y values:

The points are (1, 9.5), (2, 12.5), (3, 17), (4, 21), (5, 26)

So the means are:

x = (1 + 2 + 3 + 4 + 5) / 5 and y = (9.5 + 12.5 + 17 + 21 + 26) / 5
x = 15 / 5 and y = 86 / 5
x = 3 and y = 17.2

the slope can be calculated with this equation:

m = Σ(i = 1 to n) [(xᵢ - x)(yᵢ - y)] / Σ(i = 1 to n) (xᵢ - x)²

Since we have 5 points, we find the difference between each point and the mean and either multiply it by the difference of the y from each point or square it if it's numerator or denomintor, add all of the results, then divide the sums:

m = {[(1 - 3)(9.5 - 17.2)] + [(2 - 3)(12.5 - 17.2)] + [(3 - 3)(17 - 17.2)] + [(4 - 3)(21 - 17.2)] + [(5 - 3)(26 - 17.2)]} / [(1 - 3)² + (2 - 3)² + (3 - 3)² + (4 - 3)² + (5 - 3)²]

m = {[-2(-7.7)] + [-1(-4.7)] + [0(-0.2)] + [1(3.8)] + [2(8.8)]} / [(-2)² + (-1)² + 0² + 1² + 2²]
m = (15.4 + 4.7 + 0 + 3.8 + 17.6) / (4 + 1 + 0 + 1 + 4)
m = 41.5 / 10
m = 4.15

Now solve for the intercept of the line using this equation:

b = y - mx (these are the mean of y and the mean of x and the m we just calculated)
b = 17.2 - 4.15(3)
b = 17.2 - 12.45
b = 4.75

So the equation for the approximation line near the points would be:

y = 4.15x + 4.75

Plotting the points and the line above, the line is close to all points:

https://www.desmos.com/calculator/kxmcyi...
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ted s say: SO YOU LOOK FOR WHAT IS TERMED A " BEST FIT " LINE {caps on , sorry }....is this from a linear algebra course ?....y = 4.75 + 4.15 x....go to 'wikipedia.org', type in ' best fit line ' and read
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lludz say: ciaexbjo
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wwzar say: zbtzpfdp
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