Question

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)

Answer 1

Answer:

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

• m is the slope of the line
• b is the y-intercept (y at x = 0)

The formula of the slope is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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

∴ $x_{1}$ = 5 and  $x_{2}$ = 4

∴ $y_{1}$ = 6 and  $y_{2}$ = 8

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

∵ $m=\frac{8-6}{4-5}=\frac{2}{-1}$

∴ 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