Question

Write the equation of a line that passes through (2,7) and (-1,9)

Answer 1

`\displaystyle 2x + 3y = 25\:OR\:y = -(2)/(3)x + 8(1)/(3)`

Explanation:

First, find the rate of change [slope]:

`\displaystyle (-y_1 + y_2)/(-x_1 + x_2) = m \\ \\ (-7 + 9)/(-2 - 1) = -(2)/(3)`

Now plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula, since it is much swifter that way. It does not matter which ordered pair you choose:

9 = ⅔ + b

`\displaystyle 8(1)/(3) = b \\ \\ y = -(2)/(3)x + 8(1)/(3)`

If you want it in Standard Form:

y = −⅔x + 8⅓

+ ⅔x + ⅔x

____________

⅔x + y = 8⅓ [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

3[⅔x + y = 8⅓]

`\displaystyle 2x + 3y = 25`

_______________________________________________

7 = −⅔[2] + b

−1⅓

`\displaystyle 8(1)/(3) = b \\ \\ y = -(2)/(3)x + 8(1)/(3)`

If you want it in Standard Form:

y = −⅔x + 8⅓

+ ⅔x + ⅔x

____________

⅔x + y = 8⅓ [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

3[⅔x + y = 8⅓]

`\displaystyle 2x + 3y = 25`

** You see? I told you that it did not matter which ordered pair you choose [as long your rate of change is correct] because you will ALWAYS get the exact same result.

I am joyous to assist you anytime.