Slope Equations

Meet the silver comet.

This graph shows how it moves steadily at a constant rate.

Its motion can be described by this slope equation. Y equals point one two five x.

Let's explore what that means.

In this equation, y stands for the distance, in meters that the silver comet travels. X stands for time in seconds. And the number point one two five is the slope.

That slope tells us how fast the racer moves, how many meters it travels for each second.

A variable is written next to a value, like in this case, that means they are being multiplied. Point one two five times x.

Here's the great thing about a slope equation. Once we have that information, we can solve any problem for time or distance without even looking back at the graph.

If we wanted to know how far the silver comet travels in one minute, we can use the equation to find the answer. Start with y equals point one two five x.

Remember, x stands for the number of seconds. One minute is sixty seconds. I can substitute sixty in for x.

That gives us y equals point one two five times sixty.

When I multiply, I'm going to start by ignoring the decimal for a moment. I'll treat zero point one two five as one hundred twenty five and multiply that by sixty.

One hundred twenty five times sixty equals seven thousand five hundred.

But remember, point one two five is one thousand times smaller than one twenty five, so our product must also be one thousand times smaller.

Divide seven thousand five hundred by one thousand. That's the same as dividing by ten three times, and we get seven point five.

So y equals seven point five.

In one minute, the silver comet travels about seven point five meters.

That's the power of an equation. It tells the whole story of the racer's motion.

The equation y equals slope times x, or y equals mx in algebraic language, lets us predict the distance for any time.