Question

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

Answer 1

Answer:

$\displaystyle x - 3y = 6\:OR\:y = \frac{1}{3}x - 2$

Step-by-step explanation:

First, find the rate of change [slope]:

$\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{3 + 2}{3 + 12} = \frac{5}{15} = \frac{1}{3}$

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

$\displaystyle -2 = b \\ \\ y = \frac{1}{3}x - 2$

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

$\displaystyle -2 = b \\ \\ y = \frac{1}{3}x - 2$

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.