Select the correct function for each table, graph and equation.(6 points)

Question

Linear Nonlinear
3x−4y=27





3x2−2x=4y

Answer 1

To classify the given equations as linear or nonlinear, we can analyze each one.

1. Equation: \(3x - 4y = 27\)

   • This is a linear equation because it can be rewritten in the slope-intercept form \(y = mx + b\). Rearranging gives: \[ 4y = 3x - 27 \implies y = \frac{3}{4}x - \frac{27}{4} \]
   • Classification: Linear

2. Equation: \(3x^2 - 2x = 4y\)

   • This equation contains a term with \(x^2\), which makes it nonlinear. Rearranging gives: \[ 4y = 3x^2 - 2x \implies y = \frac{3}{4}x^2 - \frac{1}{2}x \]
   • Classification: Nonlinear

Summary

• Linear: \(3x - 4y = 27\)
• Nonlinear: \(3x^2 - 2x = 4y\)