Which is the equation of the line that passes through the points (-4, 3) and (2,-6)

1 answer:

6 0

First we have to find the slope by dividing the difference of the ys over the xs

-6 - 3 = -9 (y)
2 - -4 = 6 (x)

the slope is -9/6 or -3/2

now we plug the slop along with a set of points into the slope intercept formula (y=mx+b) to find b (the y intercept)

-6 = 2(-3/2) + b
-6 = -3 + b
-3 = b

so the equation would be y = (-3/2)x - 3

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Simplify: cos2x-cos4 all over sin2x + sin 4x

GrogVix [38]

Answer:

$\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}=\tan\left(x\right)$

Step-by-step explanation:

$\frac{\cos\left(2x\right)-\cos\left(4x\right)}{\sin\left(2x\right)+\sin\left(4x\right)}$

Apply formula:

$\cos\left(A\right)-\cos\left(B\right)=-2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)$ and

$\sin\left(A\right)+\sin\left(B\right)=2\cdot\sin\left(\frac{A+B}{2}\right)\cdot\sin\left(\frac{A-B}{2}\right)$

We get:

$=\frac{-2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\sin\left(\frac{2x-4x}{2}\right)}{2\cdot\sin\left(\frac{2x+4x}{2}\right)\cdot\cos\left(\frac{2x-4x}{2}\right)}$