To understand the meaning of the [tex]$y$[/tex]-intercept in this situation, let's break down the components of the linear relationship between the number of miles the cab travels ([tex]$x$[/tex]) and the total fee ([tex]$y$[/tex]).
Given the data points in the table, we can establish a linear relationship in the form of an equation [tex]\( y = mx + b \)[/tex] where:
- [tex]\( m \)[/tex] is the slope of the line (representing the rate per mile)
- [tex]\( b \)[/tex] is the y-intercept (representing the base fare)
For this specific problem, we found that:
- The slope ([tex]\( m \)[/tex]) is 1.5.
- The y-intercept ([tex]\( b \)[/tex]) is 12.
The slope of 1.5 means that for each additional mile traveled, the total fee increases by \[tex]$1.50.
The y-intercept of 12 means that when the number of miles traveled (\( x \)) is zero, the total fee (\( y \)) is \$[/tex]12.00. In practical terms, the [tex]$y$[/tex]-intercept refers to the base fare or the initial charge for the cab service before any distance is traveled.
So, in this situation, the [tex]$y$[/tex]-intercept (12) represents the initial fee that Tyrell has to pay just for getting into the cab, regardless of the distance traveled. This base fare accounts for the minimum service cost for starting the cab ride.
