Interpreting slope and y-intercept
About this video
A graph shows the amount of water in a hot tub as it fills, passing through (0, 15) and (5, 35). The video finds the slope 20/5 = 4 gallons per minute, the rate the tub fills, and the y-intercept 15 gallons, the amount of water in the tub at time 0.
You'll be able to
- find the slope of a line from two points and give it units.
- explain what the slope means in a real context (a rate).
- find the y-intercept and explain it as the starting amount.
Key words
- slope
- Change in y divided by change in x; here, gallons added per minute.
- y-intercept
- The y-value where the line crosses the y-axis, when x = 0.
- rate
- How fast one quantity changes compared with another, like 4 gallons per minute.
Transcript
- [Instructor] So the graph here shows the amount of water in a hot tub as it is being filled, and what I want you to do is try to figure out the slope and also figure out the y-intercept. And not just figure out what they are, but think about what their meaning is in this context.
So pause the video and try to do that. All right, so first, let's do the slope. There's many ways that you can approach the slope. One way is just think about what is the change in y for any given change in x? And we could actually figure out the slope between the two points they give us.
We could say, okay, we're going from x equals 0 to x equals 5. So this length right over here is 5 or our change in x, we could say, is 5. And then our change in y, when our change in x is 5 is this right over here, we went from 15 to 35, so this is plus 20. And I should put a plus here too 'cause if we went down, it would be negative whatever.
So what is going to be our change in y over change in x? It's going to be, this is going to be our slope, our slope is going to be equal to 20 over this 5, which is equal to 4. Now, what's the significance of that? Well, to even help us think about the significance, we could put some units here because this is in gallons, gallons here, this is in minutes, minutes.
And so this is in gallons per minute, 20 gallons per 5 minutes. So we could write that, gallons per minute. So this slope represents the rate at which the water is being filled in the hot tub. It's 4 gallons per minute. Now, what does the y-intercept represent?
Well, first of all, what is it? Well, that's where we intersect the y-axis. The y-intercept is that y value when x is equal to 0. So it's going to be y is equal to 15, y is equal to 15. Now, what does that represent? Well, it's y is equal to 15 gallons. You can't see that.
Y is equal to 15 gallons. So that's how much water is in the hot tub at times 0. That's how much we are starting with, and then we are filling it at a rate of 4 gallons.
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