# Direct linear relationship physics and technology GRAPHS IN PHYSICS 1. Published in: Education, Technology If two variables show a linear relationship theyare directly proportional to. Here we list some important examples of direct proportionalities; where we The relation between hours and minutes is so ubiquitous that most people .. The Cartesian plane and the beauty of graph paper Explore the role of technology and data in cities, and learn how you can participate in the creation of smart cities . In an introductory physics course, you'll find that directly proportional relationships show up quite a lot. A famous example of this is Newton's.

### Direct variation word problem: filling gas (video) | Khan Academy

So in this example, the change in x is always going to be 1. So in order for this function to be linear, our change in y needs to be constant because we're just going to take that and divide it by 1. So let's see if our change in y is constant. When we go from 11 to 14, we go up by 3. When we go from 14 to 19, we go up by 5, so I already see that it is not constant. We didn't go up by 3 this time, we went up by 5. And here, we go up by 7.

And here, we're going up by 9.

So we're actually going up by increasing amounts, so we're definitely dealing with a non-linear function. And we can see that if we graph it out. So let me draw-- I'll do a rough graph here. So let me make that my vertical axis, my y-axis. And we go all the way up to So I'll just do 10, 20, Actually, I can it do a little bit more granularly than that.

Dependent and Independent Variables - X or Y - Science & Math - Linear, Inverse, Quadratic

I could do 5, 10, 15, 20, 25, 30, and then And then our values go 1 through 5. I'll do it on this axis right here. They're not obviously the exact same scale, so I'll do 1, 2, 3, 4, and 5. So let's plot these points. So the first point is 1, 11, when x is 1, y is This is our x-axis.

When x is 1, y is 11, that's right about there. Units of the slope? As the speed increases, the time for the trip decreases.

## Graphing Techniques and Interpreting Graphs

Can you figure out k? What are the units of k? As the resistance increases, the current decreases. There are other functions whose graphs look like quadratics and exponentials.

Quadratic Relationship A quadratic relationship can be represented by the following equation: Shape is a parabola; has a maximum or a minimum, and is symmetric about a vertical axis.

Oscillating Relationships Oscillating relationship: B Section Learning Check 1. In an inverse relationship a hyperbola results when one variable depends on the inverse of the other. Section Learning Check 1. The line joining the first and last data points in a graph. The line joining the two center-most data points in a graph. The line drawn close to all data points as possible. The line joining the maximum data points in a graph. C Section Learning Check 1. The line drawn closer to all data points as possible, is called a line of best fit. The line of best fit is a better model for predictions than any one or two points that help to determine the line. Linear relationship Quadratic relationship Parabolic relationship Inverse relationship 21 Section Check 1.

Interpolation-- finding points between points. Extrapolation-- finding points beyond the last point. 