Final answer:
A linear equation is in the form y = mx + b, and if m = 0, our linear function will be y = b, which represents a horizontal line. Among the given options, the only function that is linear is Option A: y = mx + b, as it fits the standard form with m=0 becoming y = b.
Step-by-step explanation:
If x and y are variables, and b and m are constants, to determine which of the given functions is linear, let's recall the standard form of a linear equation, which is y = mx + b. In this form, m represents the slope of the line, and b is the y-intercept. These equations represent a straight line when graphed on the Cartesian plane.
Since we are told to assume that m = 0 and we seek a linear equation, our equation would still fit the form of y = mx + b with m being 0. Therefore, the only linear function among the given choices would be:
- Option A: y = mx + b - This is a linear function because it has no exponents on the variable x and matches the standard linear form. Since m = 0 in our case, this reduces to y = b, which represent a horizontal line on the graph.
Options B and D are not linear because they contain the term x raised to a power, which does not conform to the standard linear form. Option C is also not linear as it does not depend on x, and does not represent a line but rather a constant function.