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3 years ago

What is the equation of the line that passes through the points (1, 2) and (-2, -13)?

Mathematics

1 answer:

kenny6666 [7]3 years ago

3 0

Answer:

y = 5x - 3

Step-by-step explanation:

As we move from the point (-2, -13) to the point (1, 2), we see the x-value (the 'run') increasing by 3 and the y-value (the 'rise') increasing by 15. Therefore the slope of the line passing thru these two points is m = rise / run = 15/3, or m = 5.

Using the slope-intercept formyula y = mx + b, we find the y-intercept as follows, using 1 for x, 2 for y and 5 for m:

2 = 5(1) + b, or

b = -3

Then the desired equation is

y = 5x - 3

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mrs_skeptik [129]

Answer:

Step-by-step explanation:

If you're looking for what the half angle of the tangent of theta is, I'm a bit confused as to why you think the angle in the 4th quadrant, x, is relevant. But maybe you don't know it isn't and it's a "trick" to throw you off. Hmm...

Anyways, the half angle identity for tangent is

$tan(\frac{\theta}{2})=\frac{sin\theta}{1+cos\theta}$

There are actually 3 identities for the tangent of a half angle, but this one works just as well as either of the others do, so I'm going with this one.

If theta is in QIII, the value of -4 goes along the x axis and the hypotenuse is 5. That makes the missing side, by Pythagorean's Theorem, -3. Filling in our formula:

$tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{1+(-\frac{4}{5}) }$ which simplifies a bit to

$tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{\frac{5}{5} -\frac{4}{5} }$ and a bit more to

$tan(\frac{\theta}{2})=\frac{-\frac{3}{5} }{\frac{1}{5} }$

Bring up the lower fraction and flip it to divide to get

$tan(\frac{\theta}{2})=-\frac{3}{5}*\frac{5}{1}$ which of course simplifies to

-3. Choice A.

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