On a bicycle, Gianna rides for $5$ hours and is $66$ miles from her house. After riding for $9$ hours, she is $114$ miles away.

What is Gianna's rate? miles per hour

How far away from her house did Gianna start riding? miles $($Note that she did not start riding at her house.$)$

Write an equation of the form $d=mh+b$ to model this situation $($use variables $d$ and $h,$ where $d$ is the distance from her house in miles and $h$ is the time in hours$).$

$d=$