d = 50t — distance and time at 50 mph
Imagine a car cruising down the highway at fifty miles per hour. How far has it traveled after one, two, or three hours?
We can capture this with one rule. Let t be the time in hours and d be the distance in miles. Then d equals fifty times t.
Let's build a table to see how t and d change together.
When t is one hour, d is fifty times one — fifty miles.
When t is two hours, d is fifty times two — one hundred miles.
When t is three hours, d is fifty times three — one hundred fifty miles.
Now let's picture this on a coordinate plane. Time goes across, distance goes up.
Our first pair, one and fifty, lands here.
Two and one hundred, here.
And three and one hundred fifty, right here.
Look at the pattern: every time t grows by one hour, d grows by fifty miles. That's our rate — fifty miles per hour.
The equation d equals fifty t shows two variables changing together at a steady rate. Great work!