Answer:
[tex]\displaystyle 2x + 3y = 25\:OR\:y = -\frac{2}{3}x + 8\frac{1}{3}[/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{-7 + 9}{-2 - 1} = -\frac{2}{3}[/tex]
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
[tex]\displaystyle 8\frac{1}{3} = b \\ \\ y = -\frac{2}{3}x + 8\frac{1}{3}[/tex]
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]
[tex]\displaystyle 2x + 3y = 25[/tex]
_______________________________________________
7 = −⅔[2] + b
−1⅓
[tex]\displaystyle 8\frac{1}{3} = b \\ \\ y = -\frac{2}{3}x + 8\frac{1}{3}[/tex]
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]
[tex]\displaystyle 2x + 3y = 25[/tex]
** 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.
