Question

Consider the equation y = a - bx. If y = 6 when x = 1 and y = 0 when x = 2, find . = х

(a) the value of a and b
(b) the value of y when x = 4.​

Answer 1

see explanation

Explanation:

(a)

y =
`(a)/(x)` - bx

substitute y = 6 , x = 1 into the equation

6 = a - b → (1)

substitute y = 0 , x = 2 into the equation

0 =
`(a)/(2)` - 2b ( multiply through by 2 to clear the fraction )

0 = a - 4b → (2)

multiply (1) by - 4

- 24 = - 4a + 4b → (3)

add (2) and (3) term by term to eliminate b

- 24 = - 3a + 0

- 24 = - 3a ( divide both sides by - 3 )

8 = a

substitute a = 8 into (1) and solve for b

6 = 8 - b ( subtract 8 from both sides )

- 2 = - b ( multiply both sides by - 1 )

2 = b

Then a = 8 and b = 2

(b)

when x = 4

y =
`(8)/(4)` - 2(2) = 2 - 4 = - 2