Comparing Constant Rates 05:51 minutes

Video Transcript

Transcript Comparing Constant Rates

It’s Friday the 13th in the sleepy suburb of Shadow Hills. Tim has invited his friend, Nora, for a zombie film marathon at his place. While watching the movies, Tim and Nora realize that the zombies' speed always changes depending upon the movie. In some movies, the zombies are fast and in others, they’re really slow. This truly annoys Tim and Nora. So they want to take a closer look. To investigate the various zombie speeds, the two friends should compare constant rates. They’ve gathered information on zombies' constant rates of speed from three of their favorite films. From The Walking Elderly, we have a table from Dawn of the Dad, an equation and from 28 Months Later, a graph. Each representation includes the zombies' speeds in feet per second. Can we compare tables, to equations, to graphs? We can, if we convert the different representations into the same format. Looking at the table from Walking Elderly, we can see a constant change in distance covered by the zombies for every one second they're walking. Because the zombies have a constant rate of speed at 4 feet per 1 second we can use that rate as the slope of the graph. Therefore, using 'd' for distance and 't' for time we can express the table as the equation 'd' equals '4t'. On the graph the horizontal axis is 't', and the vertical axis is 'd'. Since we want to graph this equation, we should start at the origin and, using the slope, put a point on the graph each time we move right 1 and up 4. This represents the point (1, 4) and using the same steps of the slope, this represents the point (2, 8). We can check to see if these points are correct by matching them to our table. Because our points are correct we can now draw the line. Let's look at the next bit of information from Dawn of the Dad. We already have the equation for the zombies here: 'd' equals '8t'. We can graph it using the same steps from before. Notice that the y-intercept is zero so we can start plotting the graph at the origin.
What is the constant rate of speed for the zombies in this movie? If you said 8 feet per second, you're exactly right! We can use 8 over one as the slope. Graphically this means to go right 1 and up 8. Since we're working with a linear equation, graphing leaves us with a line. Two movies down, one movie to go. For 28 months later we already have a graph...but what's the equation? If we reverse our process from before, we can figure it out. Can you find the slope of the line? Let's examine these exact points. We can see to get these points we go to the right 4 and up one, at a constant rate. Remember the slope is the change in the vertical values over the change in the horizontal values. Which is one fourth here. But what about the y-intercept? It passes through the origin - and any line that passes through the origin has a y-intercept of zero. Therefore, our equation for the last movie is 'd' equals one-fourth 't' plus zero. But mathematicians always simplify so we can write it as 'd' equals one fourth 't'. Now that we have converted the tables, graphs, and equations to the same representations for all three movies we can compare them graphically and algebraically. First, notice that all three equations lack a y-intercept term, so they all start at the origin. Therefore, the only difference in the graphs should be their steepness represented by their slopes. When is the graph of an equation the steepest? It’s steepest when it has the highest coefficient, or, the number that represents the slope. Here, the steepest graph is represented by 'd' equals '8t'. Remember, the slopes here represents the zombies' speeds so the zombies from Dawn of the Dad are the fastest and the zombies in 28 Months Later have the slowest speed at one fourth of a foot per second. To summarize, the constant rate is the slope, which can be seen in the equation as the coefficient of your independent variable and in the graph as the steepness of the line. Tim and Nora's movie marathon is just about over. What's that? A zombie?!? That zombie is fast. Must be from Dawn of the Dad. Oh whew! It’s just Tim’s grandma...and she has pie.