Question

the equation and graph show the distance traveled by a convertible and a limousine in miles, y, as a function of time in hours, x. convertible: y = 35x compare the speeds of the two vehicles. the rate of change of the limousine is? the rate of change of the convertible. the convertible is? than the limousine.

Explanation:

Step1: Find the rate of change of the limousine

The rate of change (slope) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For the limousine, using the points \((0,0)\) and \((3,90)\), \(m=\frac{90 - 0}{3 - 0}=30\).

Step2: Compare the rates of change

The rate of change of the convertible is \(35\) (from \(y = 35x\)) and the rate of change of the limousine is \(30\).

Answer:

The rate of change of the limousine is \(less\) than the rate of change of the convertible. The convertible is \(faster\) than the limousine.