how many points on line with equation 3x+y= 15 have int coordinates and |y| < 30
a.18,b.19,c.20,d.21,e.29
a.18,b.19,c.20,d.21,e.29
If x is an integer, y = 15 - 3x will also be an integer.
Now, |y| < 30
So, |15 - 3x| < 30
So, 3*|5 - x| < 30
So, |5 - x| < 10
This means distance between x and 5 is less than 10.
So, x must be greater than (5 - 10) = -5 but less than (5 + 10) = 15
So, -5 < x < 15
So, possible number of such points = possible number of integral values of x = (15 - (-5)) - 1 = 20 - 1 = 19
Answer : B
