PrepSwift Quant Tickbox Quiz #8 (Coordinate Geometry Column 2) - Question #17

GRE Quant Problem Solving
1

I solved this by way of elimination:
Step 1: Eliminate all those with > because shaded portion is below the line
Step 2: Looking at the line, it seemed that the slope is < -1
Step 3: Write in y=mx+b format. I found the only option with m< -1 was: 2x+y </= 5

Was I correct with my approach in Step 2? Since the line was labelled also with numbers, I could conclusively say that the slope is < -1 because y>x.

Or would there be another way to do this?

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2

Find the equation of the line in the form y = mx + b. Since the region is shaded “below the line”, we use y \leq mx + b.

In other words, the right answer is simply -mx + y \leq b, using the appropriately calculated values of m and b

3

Yes, the idea of Step 2 is correct.
(Although it shouldn’t be the approach for solving, as if the options had multiple equations which satisfied this, then you would have just wasted a bit of time)