Final answer:
All options (a) 3x + 9, (b) 5x + 15, (c) 8x - 20, and (d) 12x - 20 represent linear functions, as they conform to the standard linear equation form y = mx + b, which describes a straight line with a constant slope.
Step-by-step explanation:
Understanding Linear Functions
To determine which of the given equations represents a linear function, we need to recognize that a linear equation is typically in the form y = mx + b where m is the slope and b is the y-intercept. Options (a) 3x + 9, (b) 5x + 15, (c) 8x - 20, and (d) 12x - 20, all resemble this standard form of a linear equation, therefore, they are all linear functions. The presence of only the first power of x and a constant term solidifies this conclusion. Moreover, looking at the given reference examples, such as y = -3x, y = 0.2 +0.74x, and y = 9 + 3x, confirms the pattern of linear functions.
The defining characteristic of a linear function is its constant slope and direct proportionality. Each of the mentioned equations illustrates a situation with a constant change in y for a constant change in x, leading to these equations defining straight lines on a graph.