Final answer:
y = x + 5, y = 4x - 2, and y = 9x are linear equations as they fit the form y = mx + b, where m and b represent the slope and y-intercept, respectively. y = (x - 1)(x+7) is nonlinear because it is a quadratic equation when expanded.
Step-by-step explanation:
To determine whether the given equations represent a linear or nonlinear function, we need to check if they are in the standard form of a linear equation, which is y = a + bx. In this form, b is the slope, and a is the y-intercept. A linear equation graphs as a straight line.
- y = x + 5 is a linear equation because it is in the form y = mx + b, with m = 1 (the coefficient of x) and b = 5 (the constant term). So, the correct answer is c) Linear; because it has a constant added.
- y = 4x - 2 is a linear equation because it is in the form y = mx + b, with m = 4 (the coefficient of x) and b = -2 (the constant term). So, the correct choice is a) Linear; because it is in the form y = mx + b.
- y = 9x is a linear equation because it can also be written in the form y = mx + b, with m = 9 and b = 0. Thus, the correct answer is c) Linear; because it is in the form y = mx.
- y = (x - 1)(x+7) is a nonlinear function because when you expand this, it becomes a quadratic equation, which has the form y = ax² + bx + c, where a ≠ 0. Therefore, the correct choice is d) Nonlinear; because it is a quadratic function.