Question

the rate of change of a car is decreasing linearly by 10 miles per hour. before the car started to slow down, the car was traveling at 50 miles per hour. can you use a linear model to represent the cars speed as a function of time and if so, why? what is the value for the slope and the y-intercept?

Explanation:

Step1: Determine if linear model applies

A linear model has the form $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value). The speed of the car is changing at a constant rate (decreasing by 10 miles per hour), so a linear model is appropriate because the rate of change of speed with respect to time is constant.

Step2: Find the slope

The rate of change of speed is - 10 miles per hour (negative because the speed is decreasing). In the linear equation $y=mx + b$, where $y$ is speed and $x$ is time, the slope $m=- 10$.

Step3: Find the y - intercept

Before the car started to slow down (at time $x = 0$), the speed was 50 miles per hour. In the linear equation $y=mx + b$, when $x = 0$, $y=b$. So the y - intercept $b = 50$.

Answer:

Yes, we can use a linear model. The slope is -10, and the y - intercept is 50.