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Yes sure y not
slope is the ratio of change of one line (say Y) with respect to the other (say X)
so it should be given as slope=Y/X
Now apply this to a right triangle, with angle theta and base X and vertical Y
then the slope is given as
Slope=m=Y/X=hypotenuse x sin(theta)/hypotenuse x cos(theta)
Thus
m=sin(theta)/cos(theta)=tan(theta)
Yup, the definition for tanθ is same as slope. But be mindful that the angle θ is defined as the angle between the straight line and horizontal line. this is true even when θ is larger than 90 degree.
aaronhor,
You are correct. However, the equivalence between slope and Tan is still valid. For example, in the 2nd quadrant, Tan is negative, but the run is negative and the reise is positive, so the slope is also negative. This holds true in all three quadrants as long as you are careful with the signs of the rises and runs.
Regards,
Kral.
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