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:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

• 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 = $\dfrac{4}{7}$

Plug all the given information into the equation above:

$m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\dfrac{4}{7}=\dfrac{T-5}{T-2}$

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