1. Homework: For each of the four types of relationships, find a physics equation that demonstrates that relationship and state which variables show that relationship Aim: How do we analyze relationships between variables?

2. Linear Relationship Two variables y and x are linearly related if they can be written in the form of an equation, y = mx +b (m is the slope and b is the y-intercept- the value of y when the line crosses the x-axis)

3. Non-linear relationships There are a few types of non-linear relationships that we need to know: 1. Parabolic (or Quadratic) 2. Hyperbolic (or Inverse) 3. Inverse Squared

4. Parabolic (Quadratic) Relationships Two variables x and y are in parabolic relationship if they can be expressed by an equation of the form y =ax 2 + bx + c

5. Hyperbolic (Inverse) Relationship Two variables x and y are in a hyperbolic relationship if they can be expressed in the form y = a/x.

6. Inverse Square Relationship Two variables x and y are in an inverse square relationship if they can be expressed in the form, y = a/x 2

7. Linear or Non-linear? Write down the equations. State whether x and y are linearly or non-linearly related. If non-linear, state what type of non- linear relationship. 1. y = 6x2. y = 2/x3. y = 10 + 4x 2 4. x 2 y 2 = 235. 3y = 2x + 76. 44y = 3/x 2 7. y = 0.5x + z8. y 1/2 = 8x + 89. 15x = 20y

8. Application to Physics: The Centripetal Force Fc = centripetal force r= radius v = speed of object m = mass of object Fc= (m v 2 )/r According to this equation, what is the relationship between? i)Force and mass ii) Force and speed of object iii) Force and radius of circular motion

9. Application to Physics: The Gravitational Force Linear or Non-Linear? a)Gravitational Force and mass b) Gravitational force and radial distance between the masses

10. Practice calculating slope of a line The slope of a line measures its steepness. The formula we use to calculate slope is slope = rise/run

11. Practice Problem 1: Find the slope This line goes through both of these points, (6,0) and (9,2) Slope = ???

12. Practice Problem 2: Find the slope Slope = ???

13. Practice Problem 3: Find the slope of a line that goes through points (4,7) and (2,11) Write the equation of this line.