Answer:
The value of a = 5.
the value of b = 6.
Explanation:
Given the points on the line
- (6, 10)
- (a, 8)
- (4, b)
- (2, 2)
Given that all of the points are on the same line and the line represents a linear function.
Thus, the slope between any two points must be the same.
First, determine the slope between (6, 10) and (2, 2)
(x₁, y₁) = (6, 10)
(x₂, y₂) = (2, 2)
Using the formula
Slope = m = [y₂ - y₁] / [x₂ - x₁]
= [2 - 10] / [2 - 6]
= -8 / -4
= 2
Thus, the slope of the line = m = 2
Determine the value 'a'
(x₁, y₁) = (6, 10)
(x₂, y₂) = (a, 8)
Using the slope formula to determine the value of 'a'
Slope = [y₂ - y₁] / [x₂ - x₁]
As the slope between two points is 2.
now substitute slope = 2, (x₁, y₁) = (6, 10) and (x₂, y₂) = (a, 8) in the slope formula
Slope = [y₂ - y₁] / [x₂ - x₁]
2 = [8 - 10] / [a - 6]
2(a - 6) = 8 - 10
2a - 12 = -2
2a = -2 + 12
2a = 10
divide both sides by 2
a = 5
Therefore, the value of a = 5.
Determine the value 'b'
(x₁, y₁) = (2, 2)
(x₂, y₂) = (4, b)
Using the slope formula to determine the value of 'b'
Slope = [y₂ - y₁] / [x₂ - x₁]
As the slope between two points is 2.
now substitute slope = 2, (x₁, y₁) = (2, 2) and (x₂, y₂) = (4, b) in the slope formula
Slope = [y₂ - y₁] / [x₂ - x₁]
2 = [b - 2] / [4 - 2]
2(4 - 2) = b - 2
8 - 4 =b - 2
4 = b - 2
b = 6
Therefore, the value of b = 6