Verified Answer :

olemakpadu

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 

The value of T such that (-2,5) , (0,T) , (1,1) are colinear will be 7/3.

What is slope?

A slope is a tangent or angle at a point or a slope is the intensity of inclination of any geometrical lines.

Slope = Tanx where x will be the angle from the positive x-axis at that point.

The slope could be positive or negative.

The slope is also calculated by differentiation for example slope of y = sinx will be y' = cosx.

Given,

(-2,5)  , (0,T) , (1,1)

Three points are colinear so the slope will be the same.

Slope = difference in ys coordinate/difference in x coordinate

Slope associate with (-2,5) and (0,T)

(T - 5 )/( 0 +2 )

Slope associate with (0,T) , (1,1)

(1 - 0)/( 1 - T)

Equate both points

(T - 5 )/( 0 +2 ) = (1 - 0)/( 1 - T)

T = 7/3

Hence the value of T such that all three points are colinear will be 7/3.

To learn more about slopes,

https://brainly.com/question/3605446

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