Final answer:
None of the equations 7y = 6x + 8, 4y = 8, and y + 7 = 3x are nonlinear; they all represent linear functions where y varies as a straight-line function of x.
Step-by-step explanation:
To determine which equations define y as a nonlinear function of x, we need to understand the difference between linear and nonlinear functions. A linear equation takes the form y = mx + b, where m and b are constants, and the graph of this equation is a straight line. On the other hand, a nonlinear function involves exponents, products, or other terms that result in a non-straight line when graphed.
For example, equations like y = x^2 (a quadratic equation), y = 1/x (an inverse relationship), and y = e^x (an exponential relationship) would display nonlinear relationships between y and x. Figure 1.28 in the reference materials shows examples of different types of relationship graphs, including linear and nonlinear ones.
The equations 7y = 6x + 8, 4y = 8, and y + 7 = 3x mentioned in the reference are all forms of linear equations. Thus, none of them would be considered nonlinear functions of x.