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3 years ago

The equation y + 6 = one-third (X minus 9) is written in point-slope form. What is the equation written in slope-intercept form?

Mathematics

2 answers:

uysha [10]3 years ago

7 0

Answer:

y=1/3x-9

Step-by-step explanation:

just took the test looking at scores right now :)

rosijanka [135]3 years ago

3 0

Answer:

y = $\frac{1}{3}$ x - 9

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c

Given

y + 6 = $\frac{1}{3}$ (x - 9) ← distribute

y + 6 = $\frac{1}{3}$ x - 3 ( subtract 6 from both sides )

y = $\frac{1}{3}$ x - 9 ← in slope- intercept form

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A jogger runs 140 m due west, then changes direction for the second leg of her run. At the end of the run, she is 374 m away fro

USPshnik [31]

Answer:

The length of her second displacement = 247.12 m.

The direction of her second displacement = 31.24° from west.

Step-by-step explanation:

As per the question,

From the figure as drawn below,

Let the starting point be O. After running 140 m due west, she reached at point A.

∴ OA = 140 m

And At the end of the run, she is 374 m away from the starting point at an angle of 20° north of west.

∴ OP = 374 m

We have to find the distance AP = x.

By using the cosine rule in triangle OAP

$cos \theta = \frac{OA^{2}+OP^{2}-AP^{2}}{2\times OA\times OP}$

After putting the given value, we get

$cos 20= \frac{140^{2}+374^{2}-x^{2}}{2\times 140\times 374}$

$x^{2}=140^{2}+374^{2} - 2\times 140\times 374\times cos 20$

∴ x = 247.12 m

Hence,the length of her second displacement = 247.12 m.

Again,

By using the cosine rule in triangle OAP, we get

$cos \alpha = \frac{OA^{2}+AP^{2}-OP^{2}}{2\times OA\times AP}$

After putting the given value, we get

$cos \alpha = \frac{140^{2}+247.12^{2}-374^{2}}{2\times 140\times 247.12}$

∴ α = 148.759°

Hence, the direction of her second displacement = 180° - α = 180° - 148.759 = 31.24° from west.

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