Question

The points (2a, – 4a + 3), (2b - 3, b) lie on the graph of the equation

y = -3x - 2
What are the values of a and b?
11
A a
b = 1
10
5.
B) a = b=1
2'
11 1
c) a = b
10
5
5 1
D) a =
2 5

Answer 1

The points (2a, – 4a + 3), (2b - 3, b) lie on the graph of the equation y = -3x - 2

Now,

By substituting x and y with the value of the points, we get

`- 4a + 3 = - 3(2a) - 2 \\ - 4a + 3 = - 6a - 2 \\ 6a - 4a = - 3 - 2 \\ 2a = - 5 \\ a = (( - 5))/(2) \\ \boxed{a = - 2.5}`

`\\ b =- 3(2b - 3) - 2 \\ b = - 6b + 9 - 2 \\ b + 6b = 9 - 2 \\ 7b = 7 \\ b = (7)/(7) \\ \boxed{b = 1}`

Therefore,

• The value of a is -2.5.
• The value of b is 1.

Answer 2

• a = -2.5, b = 1

Explanation:

Given line:

• y = -3x - 2

Points on the same line:

• (2a, -4a + 3) and (2b - 3, b)

Substitute x and y values of both points into equation of the line and solve for a and b:

• -4a + 3 = -3(2a) - 2 ⇒ -4a + 3 = -6a - 2 ⇒ 6a - 4a = -2 - 3 ⇒ 2a = -5 ⇒ a = -2.5
• b = -3(2b - 3) - 2 ⇒ b = -6b + 9 - 2 ⇒ b+ 6b = 7 ⇒ 7b = 7 ⇒ b = 1