Which of the following represent(s) an equation of the line passing through the points A(5, 6) and B(4, 8). Select all that apply.

A) y = -2x + 16
B) y = -2x – 4
C) 2x + y = -16
D) 2x + y = 16
E) y – 6 = -2(x – 5)

The equations that represent the equation of the line are:

y = -2x + 16 ⇒ A

2x + y = 16 ⇒ D

y - 6 = -2(x - 5) ⇒ E

Step-by-step explanation:

The slope intercept form of the linear equation is y = m x + b, where

The formula of the slope is

∵ The line is passing through points (5 , 6) and (4 , 8)

∴ = 5 and   = 4

∴ = 6 and   = 8

- Substitute them in the formula of the slope to find it

∵

∴ m = -2

- Substitute it in the form of the equation

∴ y = -2 x + b

- To find b substitute x and y in the equation by the coordinates

    of any point in the line

∵ x = 5 and y = 6

∴ 6 = -2(5) + b

∴ 6 = -10 + b

- Add 10 to both sides

∴ 16 = b

∴ y = -2 x + 16

∴ The equation of the line is y = -2x + 16

∴ A represents the equation of the line

∵ 2x + y = 16

- Subtract 2x from both sides

∴ y = -2x + 16

∴ D represents the equation of the line

∵ y - 6 = -2(x - 5)

∴ y - 6 = -2x + 10

- Add 6 to both sides

∴ y = -2x + 16

∴ E represents the equation of the line

The equations that represent the equation of the line are:

y = -2x + 16 ⇒ A

2x + y = 16 ⇒ D

y - 6 = -2(x - 5) ⇒ E

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step-by-step explanation:

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