Y-Intercept

These graphs show two racers, one much faster than the other.

The fast racer is shown on the graph in green. The line on the graph has a slope of zero point one two five.

The slow racer is represented by the graph in red, and its line has a slope of point zero five seven.

Let's see what happens when we race each of them on a one meter long track.

Welp, that's anticlimactic. When we race them for one meter, the faster racer wins easily.

We can see that in the graph. A steeper line means a faster speed, so that outcome makes sense.

Right now, both of these lines start at the origin. At time zero, both racers are at zero meters.

Let's make the race more fair. We will give the slow racer a half meter head start.

That means at zero seconds, the slow racer will be at point five meters.

On the graph, that shifts the whole line up. Let's watch that again.

Notice the slope of the line does not change. It is still point zero five seven. The racer is still moving at the same slow speed. Only the starting position changes.

This new starting position has a special name. It is called the y intercept. The y intercept shows where the line of the graph begins, its position along the y axis.

In this case, the y intercept is point five.

Now the race will be much closer. It is a fair race. I can use the graph to predict which racer will win the race and by how many seconds.

Starting with the faster racer, the line of the graph reaches one meter in eight seconds.

And the slower racer, getting that half meter head start, will reach the finish line in more than eight seconds. In fact, almost nine seconds.

So I predict the faster racer will still win, but this time by less than one second. Definitely a close race.

Let's run the race.

Both racers will begin at their start lines. The fast racer back at point zero and the slow racer getting a half meter head start.

Let the race begin in three, two, one, go.

Wow, that slow racer is so close to the finish line, but the fast one is closing ground quickly and the fast racer wins the race. And just like I predicted, it won by less than a second.

That head start really changed things. The slope or speed stayed the same, but the position of the line on the graph shifts up, creating a y intercept, and it made for a much more exciting finish.