Answer:
[tex]\displaystyle x - 3y = 6\:OR\:y = \frac{1}{3}x - 2[/tex]
Step-by-step explanation:
First, find the rate of change [slope]:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{3 + 2}{3 + 12} = \frac{5}{15} = \frac{1}{3}[/tex]
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
[tex]\displaystyle -2 = b \\ \\ y = \frac{1}{3}x - 2[/tex]
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]
[tex]\displaystyle x - 3y = 6[/tex]
_______________________________________________
−3 = ⅓[−3] + b
−1
[tex]\displaystyle -2 = b \\ \\ y = \frac{1}{3}x - 2[/tex]
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]
[tex]\displaystyle x - 3y = 6[/tex]
** 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.
