Question
In which choice is \( y \) a linear function of \( x \) ? A \( y=\sqrt{x-4}+5 \) B \( \quad y=\frac{2}{x-3} \) C \( y=7 x(x+8) \) D \( y=\frac{9-x}{6^{2}} \)
Ask by Welch Gibson. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Choice D is a linear function.
Solution
We want to find the function where y is a linear function of x; that is, it can be written in the form y = mx + b.
Choice A: y = √(x - 4) + 5
• The square root prevents this from being a linear function.
Choice B: y = 2/(x - 3)
• This is a rational function, not linear.
Choice C: y = 7x(x + 8)
• Expanding gives y = 7x² + 56x, which is quadratic (not linear).
Choice D: y = (9 - x)/(6²)
• First, note that 6² = 36. So this can be rewritten as:
y = (9 - x)/36 = (-x/36) + (9/36)
y = (-1/36)x + 1/4
This is in the form y = mx + b, with m = -1/36 and b = 1/4, hence a linear function.
Answer: Choice D is the linear function.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To determine if \( y \) is a linear function of \( x \), we want an equation in the form \( y = mx + b \), where \( m \) and \( b \) are constants. Looking at the choices: A) \( y=\sqrt{x-4}+5 \): This is not linear because of the square root function. B) \( y=\frac{2}{x-3} \): This is a rational function, not linear, as it involves the division by \( x \). C) \( y=7 x(x+8) \): This is a quadratic function because of the \( x^2 \) term when expanded. D) \( y=\frac{9-x}{6^{2}} \): This simplifies to a linear function since it can be expressed as \( y = \frac{-1}{36}x + \frac{3}{4} \). Therefore, the correct answer is **D**.
