In the rectangular coordinate system, does the line K (not shown) intersect the second quadrant?
a) The slope of K is -1/6
b)The Y intercept of K is -6.
BTW, "rectangular coordinate system" , I assume it means the Cartesian plane
1. quadrant 2: when x <0, y>0
line K : y= -1/6 x + b ( we don't know b yet)
of coz, there'll be negative values of x which produce positive y with any b
----> line K intersects 2nd quadrant
Hi Laxie, I am trying to rephrase your explanation for statement 1 . Pls let me know if I got it correct..
we are asked to find if the x<0andY>0 satisfies the equation for the line
Now if x<0 then -1/6x becomes positive and Y is positive. that makes B positive. Since the y intercept when x=o is positive , the line intercects the II quadrant...correct?
Well, like this....
in case:+ b>=0
: for every x<0 , we have -1/6 x + b > 0 coz the two terms are positive. ----> y> 0 -----> the line surely intersects quadrant 2+ b<0 :
when x< 0 , we have -1/6 x > 0 ....in some cases when the absolute value of b > -1/6x , y < 0 ....but there're certainly
values of x which make the absolute value of -1/6 x larger than that of b ----> y is positive. Since a line is infinitive, there're values of x large enough to outweigh the absolute value of this negative b ----> the line must intersect quadrant 2
A little abstract, hope you understand my explanation, if you're still confused, i'll try my better
best to explain to you