Equations

In this video, let's use the data from our ratio table in conjunction with the graph to create an equation that shows the relationship between time in seconds and distance in centimeters.

The data is moving at a constant rate, which simply means that it's increasing at a steady uniform pace. And this is evidenced by the straight line of the graph.

Our first step in writing the equation is to identify that rate of travel.

Now this is simple to find because we've already calculated the unit rate.

Every second the vehicle is traveling 25.33 centimeters.

So to find any data point, we could simply multiply the seconds by 25.33.

That is the rate.

Now let's use this to write an equation that shows the relationship between seconds and centimeters as expressed in the graph and a table.

Why is an equation so useful? Well, it can be used to find very precise information for any time or distance.

The data table shows five pieces of information.

The graph shows lots of information but only goes up to about 25 seconds and requires estimation.

Let's suppose I'm asked how long it will take the vehicle to travel 700 centimeters.

I can't just look at the graph to find an answer.

Instead, let's use a very common formula you may have even heard of it. Distance equals Rate times Time abbreviated as d equals r times t.

I will use this symbol for multiplication so I don't get confused with the other letters.

In this scenario, the d for distance corresponds to centimeters and the t for time corresponds with seconds.

For this data, the rate is 25.33. So I can say d equals 25.33 times t.

If I want to solve for seconds, I can just change up the order and say, time equals distance divided by 25.33.

Now let's put these equations to use.

If I'm asked how long will it take the vehicle to travel three meters?

I can use the ratio table to find a range I can use the graph to make an even better prediction or I can use the formula time equals distance divided by 25.33 and find the precise time.