Question

which equation represents a linear function?
options (from top to bottom, assuming the vertical list):
y = √x - 3
y = x² - 3
y = x - 3
y = 3 - x

Explanation:

Step1: Recall linear function form

A linear function has the form \( y = mx + b \), where \( m \) and \( b \) are constants, and the exponent of \( x \) is 1.

Step2: Analyze each option

• Option 1: \( y = x - 3 \) (rewritten from \( y = x - 3 \)): This is in \( y = mx + b \) form with \( m = 1 \), \( b = -3 \), exponent of \( x \) is 1.
• Option 2: \( y = x^2 - 3 \): Exponent of \( x \) is 2, so it's a quadratic function, not linear.
• Option 3: \( y = x^3 - 3 \): Exponent of \( x \) is 3, cubic function, not linear.
• Option 4: \( y = \sqrt{x} - 3 \) (or \( y = x^{\frac{1}{2}} - 3 \)): Exponent of \( x \) is \( \frac{1}{2} \), not an integer 1, so not linear.

Answer:

\( y = x - 3 \) (the first option among the given choices, assuming the first button is \( y = x - 3 \))