Part a
theta = pi/3
sin(pi/3) = sqrt(3)/2
cos(pi/3) = 1/3
tan(angle) = opposite/adjacent = rise/run = slope
tan(pi/3) = sin(pi/3)/cos(pi/3) = (sqrt(3)/2)/(1/2) = sqrt(3)
The value of k is k = sqrt(3)
This is also the slope the line y = kx because it is in the form y = mx+b with m = sqrt(3) and b = 0.
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Part b
Pick any value you want for x, and plug it in to find the paired value of y
if x = 0, then y = 0 because
y = sqrt(3)*x = sqrt(3)*0 = 0
So (0,0) is one ordered pair on the line
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If x = 1, then y = sqrt(3), since,
y = sqrt(3)*x = sqrt(3)*1 = sqrt(3)
We can say ( 1, sqrt(3) ) is another ordered pair
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If x = sqrt(3), then,
y = sqrt(3)*x = sqrt(3)*sqrt(3) = sqrt(3*3) = sqrt(9) = 3
Therefore, ( sqrt(3), 3 ) is another ordered pair
There are infinitely many ordered pairs on this line.
