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inysia [295]
3 years ago
6

What is the slope-intercept form equation of the line that passes through (2, 4) and (4, 10)?

Mathematics
2 answers:
crimeas [40]3 years ago
5 0
x_{1}=2\\y_1=4\\x_2=4\\y_2=10
equation of the line passes through two points:
<u />(x_2-x_1)(y-y_1)=(y_2-y_1)(x-x_1)\\(4-2)(y-4)=(10-4)(x-2)\\2y-8=6x-12\\2y=6x-4\\y=3x-2
lesantik [10]3 years ago
3 0
The slope is \frac {10-4}{4-2} = 3 and thus our equation becomes y-4=3*(x-2).
If we rearrange terms we get y=3x-2
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horsena [70]

\cot^4 A - \cot^2 A = 1\\\\\cot^4 A = 1 + \cot^2 A\\\\\frac{\cos^4 A}{\sin^4 A} = 1 + \frac{\cos^2 A}{\sin^2 A}\\\\\frac{\cos^4 A}{\sin^4 A} = \frac{\sin^2 A}{\sin^2 A}+\frac{\cos^2 A}{\sin^2 A}\\\\\frac{\cos^4 A}{\sin^4 A} = \frac{\sin^2 A+\cos^2 A}{\sin^2 A}\\\\\frac{\cos^4 A}{\sin^4 A} = \frac{1}{\sin^2 A}\\\\\cos^4 A = \frac{\sin^4 A}{\sin^2 A}\\\\\cos^4 A = \sin^2 A\\\\

This then means,

\cos^4 A + \cos^2 A = 1\\\\\sin^2 A + \cos^2 A = 1\\\\

which is the pythagorean trig identity. This concludes the proof.

Therefore, if \cot^4 A - \cot^2 A = 1, then \cos^4 A + \cos^2 A = 1

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2 years ago
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