A Sloped Straight Line

Slope of a line

Imagine that same car going at 30 mph. We press the accelerator gently, and the car speeds up. We keep the accelerator pressed down and watch the speed dial on the dashboard, noting the speed every 30 seconds.

After 30 seconds, the car is going 35 mph. After one minute, the car is now going 40 mph. After 90 seconds, it’s going 45 mph, and after two minutes, it’s going 50 mph. We can see that for every minute, the car speeds up by 10 mph.

Here’s the same information summarized in a table:

Let’s visualize this in a graph.

We can see that the speed increases from 30 to 60 mph at a constant rate. We can see this is a constant rate because the increments in speed are the same every half minute, and this leads to a straight line for speed.

Expression for speed

What’s the expression for the speed? To work this out, we must have speed $s=30$ at time zero. And after that, we add an extra 10 mph for every minute. So, the expression is:

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