Final answer:
The given equation, 4x² - 3x = 4x + 7, is not a linear equation because it contains a term with the variable raised to the second power, indicating it is a quadratic equation.
Step-by-step explanation:
The equation given in the question is 4x² - 3x = 4x + 7. To determine if this is a linear equation, we need to see if it can be written in the form y = mx + b, where m and b are constants, and the highest power of the variable is 1. In the given equation, the term 4x² indicates the highest power of the variable x is 2. Therefore, this is not a linear equation; instead, it is a quadratic equation. Linear equations have variables to the first power only and graph as a straight line.