Question

Use the concept of slope to find t such that the three points are collinear (-2,5)(0,T)(1,1)

Answer 1

If they are collinear, slope between any two points is the same.

Between (-2, 5) and (1, 1).

Slope = Change in y / Change in x = (1 - 5) / (1 - -2) = -4/3

Slope between (0, T) and (1, 1)

Slope = (1 - T) / (1 - 0) = -4/3

(1 - T) /1 = -4/3

1 - T = -4/3

-T = -4/3 - 1

-T = -7/3

T = 7/3  

Answer 2

(-2,5)(1,1)
slope = (y2 - y1) / (x2 - x1)
slope = (1-5) / (1 - (-2) = -4/3

y = mx + b
slope (-4/3)
(1,1)..x = 1 and y = 1
now we sub
1 = -4/3(1) + b
1 = -4/3 + b
1 + 4/3 = b
3/3 + 4/3 = b
7/3 = b

y = -4/3x + 7/3.....(0,T)...x = 0
y = -4/3(0) + 7/3
y = 7/3

check...
(1,1)(0,7/3)
slope = (7/3 - 1) / (0 - 1)
slope = (7/3 - 3/3) / -1
slope = (4/3)/-1 = -4/3

if I did this correctly, I am thinking T = 7/3