Question

(-1,19) and (3, 35)

Answer 1

Answer:

$\displaystyle \boxed{-4x + y = 23}$

Step-by-step explanation:

First, find the rate of change [slope]:

$\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2}$

$\displaystyle \frac{-19 + 35}{1 + 3} = \frac{16}{4} = 4$

Then, 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:

35 = 4[3] + b

12

$\displaystyle 23 = b \\ \\ y = 4x + 23$

Then convert to Standard Form:

y = 4x + 23

- 4x - 4x

__________

$\displaystyle -4x + y = 23$

_______________________________________________

19 = 4[−1] + b

−4

$\displaystyle 23 = b \\ \\ y = 4x + 23$

Then convert to Standard Form:

y = 4x + 23

- 4x - 4x

__________

$\displaystyle -4x + y = 23$

** 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.