[Math Revolution GMAT math practice question]

In the coordinate plane, the y-intercept of the line \(k\) is equal to twice its slope. The y-intercept is not \(0\). What is the x-intercept of the line \(k\)?

\(A. -2\)
\(B. -1\)
\(C. 0\)
\(D. 1\)
\(E. 2\)
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\(k\,\,\,:\,\,\,y = ax + 2a\,\,\,\,\,\,\left( {a \ne 0} \right)\,\,\,\,\,\,\left( * \right)\)

\(?\,\,\,\,:\,\,\,{x_p}\,\,{\rm{when}}\,\,y = 0\)

\(\left( * \right)\,\,\,\, \Rightarrow \,\,\,\,\,\,0 = a\left( {{x_p} + 2} \right)\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{a \ne 0} \,\,\,\,\,\,\,? = {x_p} = - 2\)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net

Equation of a line is y = mx +c
Since y intercept = twice of slope
So, c = 2m
y=mx+2m

TO find x intercept lets put y = 0
SO, mx+2m = 0
-> x = -2

Answer A
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