Question

Write the equation, 3x+7=2(3-y) in function form.

Answer 1

The function of the equation is f(x) =
`-(1)/(2)`
`-(3)/(2)` x

Explanation:

The function form of the linear equation is f(x) = m x + b, where

• m is the slope of the line represents the graph of the function

• b is the y-intercept

∵ The equation is 3x + 7 = 2(3 - y)

→ Simplify the right side by multiplying the bracket by 2

∵ 3x + 7 = 2(3) - 2(y)

∴ 3x + 7 = 6 - 2y

→ Add 2y for both sides

∵ 2y + 3x + 7 = 6 - 2y + 2y

∴ 2y + 3x + 7 = 6

→ Subtract 7 from both sides

∵ 2y + 3x + 7 - 7 = 6 - 7

∴ 2y + 3x = -1

→ Subtract 3x from both sides

∵ 2y + 3x - 3x = -1 - 3x

∴ 2y = -1 - 3x

→ Divide each term by 2

∴ y =
`-(1)/(2)` -
`(3)/(2)` x

→ Replace y by f(x)

∴ f(x) =
`-(1)/(2)`
`-(3)/(2)` x

∴ The function of the equation is f(x) =
`-(1)/(2)`
`-(3)/(2)` x