The equation of line k is y = mx + b, where m and b are some constants. What is the value of m? (1) (b, 2b) belongs to k. (2) (2, 2) belongs to k.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not. B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not. C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient. D. Either statement BY ITSELF is sufficient to answer the question. E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(C) Statement (1) tells us that point (b, 2b) belongs to line k. Let’s plug it in the equation of the line. 2b = mb + b. This yields b(m – 1) = 0. So either b = 0 or m = 1. We do NOT have a definite value of m if b = 0. Therefore statement (1) by itself is NOT sufficient.

Statement (2) tells us that (2, 2) belongs to k. Let’s plug it in the equation of the line. 2 = m × 2 + b. Clearly, not knowing the value of b, we can NOT find the value of m. Therefore statement (2) by itself is NOT sufficient.

When we use the both statements together, we have the following system of two equations: b(m – 1) = 0 2 = 2m + b If the solution of the first equation is b = 0, then the second one yields 2 = 2m. So in this case m = 1. If the solution of the first equation is m = 1, then the second one yields 2 = 2 + b. So in this case b = 0. Thus the solution of the system is always b = 0, m = 1. (The equation of the line is y = x). We have the definite value of m. Therefore statements (1) and (2) taken together are sufficient to answer the question. The correct answer is C. ---------- I believe that the answer to the referred question should be A. Provinding the values of (b, 2b) in the equation can be written as: 2b = mb + b b = mb (subtracting b on both sides) 1 = m (dividing both sides by b). Hence, we are able to find the value of m by the information provided by statement 1.

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