Question

in the xy-plane, does the line with equation y = 3x + 2 contain the point (r, s) ?

Answer 1

$<b>$Line with equation y=3x+2 contains the point (r,s) means that when substituting r and s in line equation: 

s=3r+2 (or 3r+2−s=0) holds true.

So basically we are asked to determine whether 3r+2−s=03r+2−s=0 is true or not.

(1) (3r+2−s)(4r+9−s)=0  either 3r+2−s=03 OR 4r+9−s=0 OR both. Not sufficient.

(2) (4r−6−s)(3r+2−s)=0 either 3r+2−s=0 OR 4r−6−s=0 OR both. Not sufficient.

(1)+(2) Both 4r+9−s=0 and 4r−6−s=0 cannot be true (simultaneously), as 4r−s can not equal to both -9 and 6, hence 3r+2−s=0must be true. Sufficient.


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