# SAT Math Multiple Choice Question 614: Answer and Explanation

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**Question: 614**

**14.** If *k* > 2, which of the following could be the graph of *y* + *x* = *k*(*x* - 1) in the *xy*-plane?

- A.
- B.
- C.
- D.

**Correct Answer:** B

**Explanation:**

**B**

**Algebra (graphs of linear equations) HARD**

Given equation:

*y* + *x* = *k*(*x* - 1)

Subtract *x*:

*y* = *k*(*x* - 1) - *x*

Distribute:

*y* = *kx* - *k* - *x*

Collect like terms:

*y* = (*k* - 1)*x* - *k*

The slope of this line is *k* - 1 and its *y*-intercept is - *k*. If *k* > 2, then *k* - 1 > 1, and - *k* < -2. In other words, the slope of the line is greater than 1 and the *y*-intercept is less than -2. The only graph with these features is the one in choice (B).