Question

The graph of a function must be linear if it has what characteristic?

A. It passes through the origin.
B. It crosses the x-axis more than once.
C. It crosses the y-axis exactly once.
D. It has a constant slope.

Answer 1

A function's graph is linear if it has a constant slope, with every unit change in x corresponding to a consistent change in y.

Step-by-step explanation:

The graph of a function must be linear if it has a characteristic of having a constant slope. A linear graph can be represented by the equation y = a + bx, where 'b' represents the slope and 'a' represents the y-intercept. If a line has a constant slope, it means for any given change in 'x', the change in 'y' is always the same, which is the definition of a linear function. This is evident in a graph where the slope remains the same throughout, such as when there is a rise of 3 on the vertical axis for every increase of 1 on the horizontal axis, illustrating that the slope is uniform all along a straight line.