Joe claims that the equation 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.

1 answer

The equation \( y = 2x + b \) is in the slope-intercept form of a linear equation, where \( m = 2 \) (the slope) and \( b \) (the y-intercept) can be any real number. The presence of \( b \) does not affect the linearity of the equation; it simply shifts the graph up or down.

Therefore, Joe's claim that the equation represents the graph of a straight line is true for all values of \( b \).

The correct answer is:

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