# how does m = b (or slope=y-intercept

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• February 14th 2011, 08:50 PM
thejollywag
how does m = b (or slope=y-intercept
How can I prove that COVAR(x,y)/VAR(x) = b? I'm pretty sure the first part equals m, but I don't see how the slope and y-intercept can be the same thing, unless their both zero.

Any nudge in the right direction would be greatly appreciated.
• February 14th 2011, 09:02 PM
pickslides
My understanding is, for $\displaystyle y=a+bx$

then $\displaystyle a=\bar{y}-b\bar{x}, b= \frac{cov(x,y)}{var(x)}$

So this works if you call the equation $\displaystyle y=mx+c$ , many text books do.
• February 15th 2011, 08:27 AM
thejollywag
Thanks, pickslides!