Question

Which equation represents the line that passes through the points (-3,-3) and (12,2)?

Answer 1

`\displaystyle x - 3y = 6\:OR\:y = (1)/(3)x - 2`

Explanation:

First, find the rate of change [slope]:

`\displaystyle (-y_1 + y_2)/(-x_1 + x_2) = m \\ \\ (3 + 2)/(3 + 12) = (5)/(15) = (1)/(3)`

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

2 = ⅓[12] + b

4

`\displaystyle -2 = b \\ \\ y = (1)/(3)x - 2`

If you want it in Standard Form:

y = ⅓x - 2

- ⅓x - ⅓x

_________

−⅓x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−3[−⅓x + y = −2]

`\displaystyle x - 3y = 6`

_______________________________________________

−3 = ⅓[−3] + b

−1

`\displaystyle -2 = b \\ \\ y = (1)/(3)x - 2`

If you want it in Standard Form:

y = ⅓x - 2

- ⅓x - ⅓x

_________

−⅓x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−3[−⅓x + y = −2]

`\displaystyle x - 3y = 6`

** 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.