find the number of points on a straight line between points -4,11 to 16,-1 whose coordinates are positive integers
Answers
Answer:
Number of points = 2
Step-by-step explanation:
Equation of the line passing through two points and is
Thus, the equation of the line passing through (-4, 11) and (16, -1) is
This line touches the x-axis at
3x = 43 or x = 14.33
In between x = 0 to x = 14.33, the positive integral values of x = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
The line touches the y-axis at
5x = 43 or y = 8.6
In between y = 0 to y = 8.6, the positive integral values of y = 1, 2, 3, 4, 5, 6, 7, 8
For y = 1
3x + 5 = 43 ⇒ x = 12.66 (not an integer)
For y = 2
3x + 10 = 43 ⇒ x = 11 (which is an integer)
For y = 3
3x + 15 = 43 ⇒ x = 9.33 (not an integer)
For y = 4
3x + 20 = 43 ⇒ x = 7.67 (not an integer)
For y = 6
3x + 30 = 43 ⇒ x = 4.33 (not an integer)
For y = 7
3x + 35 = 43 ⇒ x = 2.67 (not an integer)
For y = 8
3x + 40 = 43 ⇒ x = 1 (which is an integer)
Therefore, there are two points, whose coordinates are positive integers.
Answer:
The equation of the line is y−11=(11+1−4−16)(x+4)=−35(x+4). This means 3x+5y=43.
Clearly (1,8) is a point on the line such that x and y are both positive integers, and other such points are found by increasing x by 5 and decreasing y by 3. We then see that the only other such points are (6,5) and (11,2).
Step-by-step explanation: