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

Question

Which statement best classifies Joe's claim?

options:

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

The equation \( y = 2x + b \) represents the equation of a straight line in slope-intercept form, where \( 2 \) is the slope and \( b \) is the y-intercept. The value of \( b \) can be any real number and will still define a line.

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

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