Wayne plays guitar in a rock band. apart from playing for his band, he has played guitar on 10 albums by other artists. suppose that wayne's band releases an album every 4 years. the function y = 0.25x + 10 represents the total number of albums wayne would play guitar on, y, with respect to the number of years, x. the rate of change of this function , and its graph is . so, the function is function. a: constant : non-constant : decresing b: straight line : curve c: constant : linear : nonlinear

The correct answers are:

A) constant
B) straight line
C) linear

Explanation:

The equation y=0.25x+10 is in slope-intercept form, y=mx+b where m is the slope and b is the y-intercept.  The slope is the rate of change.  The number in our equation that is in place of m is 0.25.  This means for every change in x, the graph will go up 0.25.  The rate of change is the same throughout the entire function, so this is a constant rate of change.

Since the rate of change is constant, the graph will be a straight line.  A constant rate of change means there is the same distance between every two points on the graph; this is only true of a straight line.

Since the graph is a straight line, the function is linear by definition.