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3 years ago

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

Mathematics

1 answer:

natka813 [3]3 years ago

4 0

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

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

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.

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2 years ago

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Symmetric: We need to prove that A↔B implies B↔A. As A↔B there exists an invertible matrix P such that $A=P^{-1}BP$ . In this equality we can perform a right multiplication by $P^{-1}$ and obtain $AP^{-1} =P^{-1}B$ . Then, in the obtained equality we perform a left multiplication by P and get $PAP^{-1} =B$ . If we write $Q=P^{-1}$ and $Q^{-1} = P$ we have $B = Q^{-1}AQ$ . Thus, B↔A.

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