Question

A direct variation function contains the points (–9, –3) and (–12, –4). Which equation represents the function?

Answer 1

Answer:

$\displaystyle y = \frac{1}{3}x$

Step-by-step explanation:

First, find the rate of change [slope]:

$\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{3 - 4}{9 - 12} = \frac{1}{3}$

Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula since you get it done much swiftly that way. It does not matter which ordered pair you choose:

−4 = ⅓[−12] + b

−4

$\displaystyle ±0 = b \\ \\ y = \frac{1}{3}x$

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−3 = ⅓[−9] + b

−3

$\displaystyle ±0 = b \\ \\ y = \frac{1}{3}x$

**You see? I told you it did not matter which ordered pair you choose because you will ALWAYS get the exact same result.

I am joyous to assist you anytime.

Answer 2

Answer:

The answer is...

Step-by-step explanation:

y = 1/3x

--or--

y = x/3

Both forms of writing are equivalent, so either choice would be correct. I hope this helps!