Question

Find the equation of the line that passes through (-2, -5) and (1, 7).

Answer 1

`\displaystyle 4x - y = -3, -4x + y = 3\:OR\:y = 4x - 3`

Explanation:

First, find the rate of change [slope]:

`\displaystyle (-y_1 + y_2)/(-x_1 + x_2) = m \\ \\ (5 + 7)/(2 + 1) = (12)/(3) = 4`

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:

7 = 4 + b

`\displaystyle 3 = b \\ \\ y = 4x + 3`

If you want it in Standard Form:

y = 4x + 3

- 4x - 4x

_________

`\displaystyle -4x + y = 3\:OR\:4x - y = -3`

_______________________________________________

−5 = 4[−2] + b

−8

`\displaystyle 3 = b \\ \\ y = 4x + 3`

If you want it in Standard Form:

y = 4x + 3

- 4x - 4x

_________

`\displaystyle -4x + y = 3\:OR\:4x - y = -3`

** 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.