Answer
(a) $d=48 t$
(b) the graph is on the figure below
(c) the slope is $48$. It represents velocity in miles per hour.
Work Step by Step
The distance traveled $d$ will be a linear function of time:
$$d=vt+d_0$$
where $v$ and $d_0$ are constants.
(a) We have to find $v$ and $d_0$. When $t=0$ then we need that $d=0$ because Jason hasn't traveled any distance:
$$0=v\cdot0+d_0\Rightarrow d_0=0.$$
Now we have $d=vt.$
To find $v$ note that for $50$ minutes which is $50/60=5/6$ hours Jason travels the distance of $40$ miles so we have
$$40=v\cdot \frac{5}{6}\Rightarrow v=48.$$
This means that the distance traveled in terms of elapsed time is
$$d=48t$$
where $d$ is in miles and $t$ is in hours.
(b) The graphs contains the origin because when $t=0$ then $d=48\cdot0=0$. Further, when $t=1$ then $d=48\cdot 1=48$ so we just draw the line starting at the origin and passing through the point $(1,48)$. This graph is on the figure below.
(c) The slope is the constant that multiplies the variable $t$ which is in this case $v=48$. It says the distance in miles that Jason travels for one hour i.e. the velocity in miles per hour.
