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Answer:
The function of the equation is f(x) = [tex]-\frac{1}{2}[/tex] [tex]-\frac{3}{2}[/tex] x
Step-by-step explanation:
The function form of the linear equation is f(x) = m x + b, where
∵ 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 = [tex]-\frac{1}{2}[/tex] - [tex]\frac{3}{2}[/tex] x
→ Replace y by f(x)
∴ f(x) = [tex]-\frac{1}{2}[/tex] [tex]-\frac{3}{2}[/tex] x
∴ The function of the equation is f(x) = [tex]-\frac{1}{2}[/tex] [tex]-\frac{3}{2}[/tex] x