Points (x,y)
$$(\color{red}{4},\color{green}{5})$$
$$(\color{red}{10},\color{green}{10})$$
Step 1: General Equation
$$y=mx+b$$
Step 2: Slope Work (m)
$$m=\frac{y_1 - y_2}{x_1-x_2} = \frac{\color{green}{5-10}}{\color{red}{4-10}} = \frac{-5}{-6} = \frac{5}{6}$$
m =
$$\color{purple}\frac{5}{6}$$
Step 3: General Equation (with m)
$$y = \color{purple}{\frac{5}{6}} \color{black}x + b$$
Step 4: y-Int Work (b)
Substitution Point:
$$(\color{red}{4},\color{green}{5})$$
Work:
$$ \color{green}{5} \color{black}= \frac{5}{6}\color{red}{(4)} \color{black}+b $$
$$ 5 = \frac{20}{6}+b $$
$$ \color{orange}\frac{5}{3} \color{black} = b$$
Step 5: Final Equation
$$y=\color{purple}\frac{5}{6}\color{black}x+\color{orange}\frac{5}{3}$$
Step 6: Domain
$$\left\{\color{red}4\color{black}\le x\le \color{red}10\color{black}\right\}$$