To know the slope we need to know the two coordinate points of each line.
With the help of both setms we can get this.

Amit

Oh yes, that is the definition of slope, change in y/change in x.

.........but I'm assuming you used a drawing to answer the question instead of getting the actual slope. So, if the Y-int of one line is greater than than of the other line, the line with the greater y-int is steeper and has a higher slope?

True, a line with higher slope gets steeper...
but i didn't use any drawing or graph.

When two stems need to be combined, then we just need to see whether
the ans is achievable.

Amit

Hi Medea,

Well, I guess you are right - a line with higher y intercept would have an obtuse angle with the X axis (as it lies in the first quadrant)i.e a negative slope(change in Y/change in X=tan(angle made by the line with the x axis)as tan(obtuse angle(90<x<180) ='-'. And any line intersecting this line at (5,1) will either have an angle greater than than the angle made by N when obtuse(i.e >90) or any angle between 0 & 90 , and in both these cases the Tan of the angle would be > than the one made by N

therefore we can say that the slope of N would be less than the line P when the intersection point is (5,1) & N is the line which makes a higher Y intercept.

thanks,
Kiran

I have a slightly algbric approach.

For each line we can say :

Line N:
y-y1 = M (x-x1) --> equation of a st line

using 5,1

y-1 = M ( x - 5)

or y = Mx - (5M+1)

Line P:
y-y1 = m (x-x1) --> equation of a st line

using 5,1

y-1 = m ( x - 5)

or y = mx - (5m+1)

Using statement 2 we know

Y intercept of N is greater than that of P
hence from the weird stuff done in statement one we can say

-(5M+1) > - (5m+1)

hence you can get the ratio of M/m or m/M ---> Solvable.