# SAT Math Multiple Choice Question 792: Answer and Explanation

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**Question: 792**

**12.** If *w* is an integer less than –1, which of the following could be the graph of *x* + *wy* = *wx* – *y* – 3?

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

**Correct Answer:** C

**Explanation:**

**C**

**Difficulty:** Hard

**Category:** Heart of Algebra / Linear Equations

**Strategic Advice:** When matching a graph to a linear equation, focus on putting the equation in slope-intercept form (*y* = *mx* + *b*) so you can determine what the graph should look like.

**Getting to the Answer:** Start by collecting the *y* terms on the left side of the equation and the *x* terms on the right (don't worry about *w* yet):

*x* + *wy* = *wx* - *y* - 3

*wy* + *y* = *wx* - *x* - 3

Next, factor out *x* and *y*, and then divide both sides by the coefficient of *y* so that it's in slope-intercept form:

The equation represents a line with a slope of and a *y*-intercept of -. Because you're given that *w* is an integer less than -1, both the slope and the *y*-intercept of the line are positive (pick an easy number, such as -2, to plug in for *w* if you're not certain). This means the line is increasing (going up) from left to right and crosses the vertical axis above 0. The only choice that contains a graph with these characteristics is (C).