Final answer:
The function y = -2x - 8 represents a linear equation, which when graphed, will display as a straight line with a negative slope. Option (a) is the correct choice for the type of equation, distinguishing it from quadratic, trigonometric, and exponential functions.
Step-by-step explanation:
The equation given is y = -2x - 8, which is a form of a linear equation and represents option (a). To recognize that this is a linear equation, consider the general form of a linear equation, which is y = a + bx, where a is the y-intercept and b is the slope of the line. In this case, the slope b is -2 and the y-intercept a is -8. The negative slope indicates that the line will slope downward to the right when graphed on a coordinate plane, typical for linear equations where b is negative.
Linear equations are characterized by creating straight lines when graphed, and they are different from quadratic equations (which form parabolas), trigonometric functions (involving sine, cosine, etc.), and exponential functions (which typically involve growth or decay processes). Each of these different types of equations produces distinct shapes when graphed. The linear equation, y = -2x - 8, is a clear representation of a straight line graph with a negative slope, so option (a) is the correct choice.