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Find T given that the line segment joining:

(2,5) and (T, T) has gradient 4/7

User Dastin
by
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1 Answer

27 votes
27 votes

Key Concepts

  • Solving for the slope/gradient
  • Systems of equations

The slope (or gradient) can be solved by using this equation:


m=(y_2-y_1)/(x_2-x_1)

  • m = slope

  • (x_1,y_1) and
    (x_2,y_2) are two points that fall on the line

Solving the Question

We're given:

  • Line passes through (2,5) and (T,T)
  • Gradient =
    (4)/(7)

Plug all the given information into the equation above:


m=(y_2-y_1)/(x_2-x_1)\\\\(4)/(7)=(T-5)/(T-2)

This means that T - 5 must equal 4 and T - 2 must equal 7.


T-5=4


T-2=7

Isolate T:


T=5+4


T=9


T=7+2


T=9

Answer

T = 9

User Adam Gerard
by
2.7k points