sana.noor wrote:The slope of the line passing through the point (5, 5) is 5/6. All of the following points could be on the line except
A. (2.5, 2)
B. (11, 10)
C. (8, 7.5)
D. (-1, 0)
E. (-7, -5)

Answer choice A: (2.5, 2)
Slope = (5-2)/(5-2.5) = 3/2.5 = 6/5.
Since the resulting slope is not 5/6, (2.5, 2) cannot be on the line.

The correct answer is A.

The other four answer choices each yield a slope of 5/6:
B: (10-5)/(11-6) = 5/6.
C: (7.5-5)/(8-5) = (2.5)/3 = 5/6.
D: (0-5)/(-1-5) = -5/-6 = 5/6.
E: (-5-5)/(-7-5) = -10/-12 = 5/6.

Another way to do this:

Most lines (lines that aren't vertical or horizontal) have equations of the form y = mx + b, where m is the slope, b is the y-intercept, and x and y are coordinates of a point on the line.

If we have a point (5, 5) on a line with slope 5/6, we could write this equation

y = mx + b

then plug in x, y, and m

5 = (5/6)*5 + b

solve for b

b = 5/6

and find the equation of the line

y = (5/6)x + 5/6

Any point whose (x,y) values satisfy this equation is on the line.

(2.5, 2) does not satisfy the equation:

2 = (5/6)*(2.5) + 5/6 ... is not correct, so this point is NOT on the line

But (8, 7.5) does:

7.5 = (5/6)*8 + 5/6

so the point (8, 7.5) is the on the line.