Multiple Choice Question

Question

Joe claims that the equation
, 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

To analyze Joe's claim, we need to understand the structure of the equation given. The equation is not fully written in your question, but a common format could be something like \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

If the equation Joe is referring to can be rearranged to fit the linear format:

1. If b = 0, the equation still represents a straight line (it passes through the origin).
2. If b is any other real number, the equation still describes a straight line (it would intersect the y-axis at that value).

Given the provided options, we can conclude:

• A is incorrect because \( b = 0 \) does represent a straight line.
• B is correct because the equation represents a straight line for all values of \( b \).
• C is incorrect because it does represent a straight line for some values of \( b \).
• D is incorrect because the line still exists when \( b \) is 0.

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

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