IN WHAT RATIO DOES THE LINE x-y-2=0 divide the line segment joining (3,-1) and (8,9) ?

thnkz

Consider the "journey" from (3, -1) to (8, 9). 
The x-coordinate increases by 5, while the y-coordinate increases by 10. 
Quick mental trial-and-error tells us that the two points lie on the line y = 2x - 7 

Now we want the point of intersection of y = 2x - 7 and x - y - 2 = 0 

Using substitution: 
x - y - 2 = 0 
x - (2x - 7) - 2 = 0 
-x + 5 = 0 
x = 5 

y = 2(5) - 7 
y = 3 

The point of intersection is (5, 3). 
The three points under consideration are (3, -1), (5, 3) and (8, 9). 
Just dealing with x-coordinates: from 3 to 5 = 2 units, and from 5 to 8 = 3 units. 

SOLUTION: the straight line x - y - 2 = 0 divides the line segment (3,-1) to (8,9) in the ratio 2:3 

k = 2/3 
k= 2:3

Aishwary answer 2: 3 is write

2/3

Ratio is 2:3

Ratio 2:3

Here is the answer