There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).
In this problem we have a line that passes through two points on a Cartesian plane and herein we must check if that line contains at least one point with integer coordinates. First, determine the equation of the line:
Slope
m = [6.9 - (- 8.5)] / (13.8 - 5)
m = 7 / 4
Intercept
b = - 8.5 - (7 / 4) · 5
b = - 69 / 4
The equation of the line is y = (7 / 4) · x - 69 / 4.
Second, evaluate the equation of the line at different integers:
x= 6
y = (7 / 4) · 6 - 69 / 4
y = - 27 / 4
x = 7
y = (7 / 4) · 7 - 69 / 4
y = - 5
x = 8
y = (7 / 4) · 8 - 69 / 4
y = - 13 / 4
x = 9
y = (7 / 4) · 9 - 69 / 4
y = - 3 / 2
x = 10
y = (7 / 4) · 10 - 69 / 4
y = 1 / 4
x = 11
y = (7 / 4) · 11 - 69 / 4
y = 2
x = 12
y = (7 / 4) · 12 - 69 / 4
y = 15 / 4
x = 13
y = (7 / 4) · 13 - 69 / 4
y = 11 / 2
There are at least two integer points in the line that passes through (5, - 8.5) and (13.8, 6.9).
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