Question

Write an equation for the line that contains the points (5,3) and (8,9)

Answer 1

`-2x + y = -7\:or\:y = 2x - 7`

Step-by-step Step-by-step explanation:

First find the rate of change [slope]:

`(-y_1 + y_2)/(-x_1 + x_2) = m`

`(-3 + 9)/(-5 + 8) = (6)/(3) = 2`

Now plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because you get it done much swiftly. It does not matter which ordered pair you choose:

9 = 2[8] + b

16

`-7 = b \\ \\ y = 2x - 7`

If you want it in Standard Form:

y = 2x - 7

- 2x - 2x

_________

`-2x + y = -7`

_______________________________________________

3 = 2[5] + b

10

`-7 = b \\ \\ y = 2x - 7`

y = 2x - 7

- 2x - 2x

_________

`-2x + y = -7`

** 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.