Answer :

theleangreenbean

Key Concepts

  • Solving for the slope/gradient
  • Systems of equations

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

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

  • m = slope
  • [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are two points that fall on the line

Solving the Question

We're given:

  • Line passes through (2,5) and (T,T)
  • Gradient = [tex]\dfrac{4}{7}[/tex]

Plug all the given information into the equation above:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\dfrac{4}{7}=\dfrac{T-5}{T-2}[/tex]

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

[tex]T-5=4[/tex]

[tex]T-2=7[/tex]

Isolate T:

[tex]T=5+4[/tex]

[tex]T=9[/tex]

[tex]T=7+2[/tex]

[tex]T=9[/tex]

Answer

T = 9

Other Questions