Question

Find T given that the line segment joining:

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

Answer 1

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