Question

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

Answer: y = x/3

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Answer 1

`\displaystyle y = (1)/(3)x`

Step-by-step explanation:

First, find the rate of change [slope]:

`\displaystyle (-y_1 + y_2)/(-x_1 + x_2) = m \\ \\ (3 - 4)/(9 - 12) = (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 = (1)/(3)x`

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−3 = ⅓[−9] + b

−3

`\displaystyle ±0 = b \\ \\ y = (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

The answer is...

Explanation:

y = 1/3x

--or--

y = x/3

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