Q: Write an equation of the form
M(V) = _________ * log(P) + ___________
which is consistent with the data in the graph.
Looking at the line drawn on the diagram, I can pick out
the endpoints
(0.6, -3.0) and (2.0, -6.5)
The slope of the line connecting them is approximately
(-6.5 - (-3.0) ) -3.5
slope = ---------------- = ------- = -2.5
( 2.0 - 0.6 ) 1.4
If we plug into the equation
-3.0 = (-2.5 * 0.6) + X
and solve for "X", we can find the y-intercept. It turns out
X = -1.5
So the relationship between period and absolute magnitude
is approximately
M(V) = -2.5 * log(P) - 1.5