Question 1202666: identify the constant of proportionality from the graph (2,1) and (10,5) Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:Answer by josgarithmetic(39630) (Show Source):
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Let's find the slope
m = (y2 - y1)/(x2 - x1)
m = (5 - 1)/(10 - 2)
m = 4/8
m = 1/2
m = 0.5
The slope is 0.5 or 1/2.
Then let's use point-slope form to determine the equation
y - y1 = m(x - x1)
y - 1 = 0.5(x - 2)
y - 1 = 0.5x - 1
y = 0.5x - 1 + 1
y = 0.5x
The equation of the line through those two points is y = 0.5x
Equations in the format y = kx are known as direct variations.
k = 0.5 = 1/2 is the constant of proportionality
It is also the slope of the line.
All direct variation equations go through the origin.
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