Question

module 6 & 3 test
which equation represents a linear function?
○ xy=15
○ y=3x²-6
○ 4y=3^x -7
○ 4x=3(y - 1)

Explanation:

Step1: Recall linear function form

A linear function has the form \( y = mx + b \) (or can be rewritten to this form), where \( m \) and \( b \) are constants, and the highest power of \( x \) is 1.

Step2: Analyze each option

• Option 1: \( xy = 15 \) can be rewritten as \( y=\frac{15}{x} \), which is a rational function, not linear.
• Option 2: \( y = 3x^2 - 6 \) has \( x^2 \), so it's a quadratic function (degree 2), not linear.
• Option 3: \( 4y = 3^x - 7 \) has an exponential term \( 3^x \), so it's an exponential function, not linear.
• Option 4: \( 4x = 3(y - 1) \)
• Expand: \( 4x = 3y - 3 \)
• Rearrange to solve for \( y \): \( 3y = 4x + 3 \) → \( y=\frac{4}{3}x + 1 \), which is in the form \( y = mx + b \) (linear function form).

Answer:

\( 4x = 3(y - 1) \) (the last option)