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
∵ 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