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tatyana61 [14]
4 years ago
8

Write the slope intercept inequality (0,2) (-1,-2)​

Mathematics
1 answer:
I am Lyosha [343]4 years ago
3 0

Hey there! :)

(0, 2) & (-1, -2)

Slope-intercept form is : y=mx+b , where m=slope, b=y-intercept

First, we must find the slope using the slope formula, which is :

m = y2-y1/x2-x1

Where y2 = -2 ; y1 = 2 ; x2 = -1 ; x1 = 0

Now, let's plug and chug! :)

m = (-2 - 2) / (-1 - 0)

Simplify.

m = -4/-1 --> Therefore, our slope is : m = 4

Now that we have the slope, we can plug this (and our original coordinates) into point-slope form, which is : y - y1 = m(x - x1) -> use the coordinates (0, 2)

y - 2 = 4(x - 0)

Simplify.

y - 2 = 4x

Add 2 to both sides.

<u>y = 4x + 2</u>

Hope this helped! :)

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See below for step-by-step proof.

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\textsf{Given expression}:

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\implies (\cos^2 \theta)^3+(\sin^2 \theta)^3

\textsf{Use the identity}\quad a^3+b^3=(a+b)^3-3ab(a+b):

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\textsf{Use the identity}\quad \sin^2 \theta + \cos^2 \theta=1:

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\textsf{Use the identity}\quad \sin 2 \theta=2 \sin \theta \cos \theta \implies \dfrac{1}{2}\sin 2 \theta= \sin \theta \cos \theta:

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\implies 1-\dfrac{3}{4} \sin^2 2 \theta

\textsf{Use the identity}\quad \sin^2 2\theta + \cos^2 2\theta=1 \implies \sin^2 2\theta=1-\cos^2 2\theta

\implies 1-\dfrac{3}{4} \left(1-\cos^2 2 \theta\right)

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\textsf{Factor out }\dfrac{1}{4}:

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\implies \dfrac{1}{8}\left(5+3\cos 4 \theta\right)

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2 years ago
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