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

Options

A.
B.
C.
D.

Answer

C

Explanation

Difficult: 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 should look like.
Getting to the Answer: Start by collecting the y terms on the left side of the equation and the x term on the rigth (don't worry abour w yet).
`x+wy=wx-y-3`
`xy+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:
`y(w+1)=x(w-1)-3`
`y=x(w-1)/(w+1)-(3)/(w+1)`
The equation represents a line with a slope of `(w-1)/(w+1)` and a y-intercept of `-(3)/(w+1)`. 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 th vertical axis above 0.The only choice that contains a graph with these charactreristic is (C).