Joe claims that the equation

Question

y = 2x + b, where b is a real number, represents the graph of a straight line.

Which statement best classifies Joe's claim?
A.
Joe's claim is true only when b is 0.

B.
Joe's claim is true for all values of b.

C.
Joe's claim is not true for any value of b.

D.
Joe's claim is true only when b is not zero.

Answer 1

Joe's claim is that the equation \( y = 2x + b \), where \( b \) is a real number, represents the graph of a straight line.

This equation is in the slope-intercept form \( y = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept. In this case, the slope \( m = 2 \) and the y-intercept \( c = b \).

Since a linear equation will always represent a straight line for any real value of \( b \), we can conclude that Joe's claim is true for all values of \( b \).

Thus, the best classification of Joe's claim is:

B. Joe's claim is true for all values of b.