Question

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 is______ , and its graph is a______ . So, the function is a________ function.

A: constant
: non-constant
: decresing

B: straight line
: curve

C: Constant
: linear
: nonlinear

Answer 1

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.

Answer 2

Answer:

A, B, and B

Step-by-step explanation: