Question

Find the number of points on the straight line between points (-4.11) to (16.-1) whose coordinates (both x and y coordinates are positive integer
Options
2
3
4
5​

Answer 1

Answer:

The slope of the line is,

16−(−4)

−1−11

=

20

−12

=

5

−3

Thus, the eqn of the line is,

y−11=

5

−3

(x−(−4))=

5

−3

x

5

−12

=

5

−1

(3x+12)

y is am integer precisely when 3x+12 is a multiply of 5, which is when (x+4) is a multiple of 5

These values of x occur 5 units apast, between −4 and 6 they arn't −4,1,6,11 and 16 and corresponding y− coordinates are 11,8,5,2 and −1.

They values of x between −4 and 6 that give integral values of y must be −4,1,6,11 and 16. The corresponding y− coordinates are 11,8,5,2 and −1.

The line segment constants exactly 3 points whose coordinates are path positive integers.