Question

A car is traveling at 45mi/h, Write an equation that models the total distance (d) traveled after (h) hours. What is the graph of the equation

Answer 1

A car is traveling at 45mi/h, Write an equation that models the total distance (d) traveled after (h) hours. What is the graph of the equation

Answer 2

Well, if the speed is constant, it means we pass the same amount of distance every hour.
In our case our speed is \(45_{mph}\) which means the car passes 45 miles every hour it travels.
If it would travel half an hour it would pass:
$$45_{mph} \cdot \frac{30_{minutes}}{60_{minutes}} = 45_{mph} \cdot \frac{1}{2} = 22.5_{mph}$$
If it would travel for 20 minutes then:
$$45_{mph} \cdot \frac{20_{minutes}}{60_{minutes}} = 45_{mph} \cdot \frac{1}{3} = 15_{mph}$$
So we can see that the distance we pass is basically a multiply of the time we travel.
That is pretty much defined from the definition of speed, because at 45 miles per hour we pass 45 miles every hour we travel.
So basically:
$$
45_{mph} \cdot h = d
$$ Where \(h\) is total time (in hours) traveled and \(d\) total distance (in miles).
This is a linear graph.