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?

Linear RelationshipTwo 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)

Non-linear relationshipsThere are a few types of non-linear

relationships that we need to know:1.Parabolic (or Quadratic)2.Hyperbolic (or Inverse)3.Inverse Squared

Parabolic (Quadratic) RelationshipsTwo variables x and y are in parabolic

relationship if they can be expressed by an equation of the form y =ax2 + bx + c

Hyperbolic (Inverse) RelationshipTwo variables x and y are in a hyperbolic

relationship if they can be expressed in the form y = a/x.

Inverse Square RelationshipTwo variables x and y are in an inverse

square relationship if they can be expressed in the form, y = a/x2

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 = 6x 2. y = 2/x 3. y = 10 + 4x2

4. x2y2 = 23 5. 3y = 2x + 7 6. 44y = 3/x2

7. y = 0.5x + z 8. y1/2 = 8x + 8 9. 15x = 20y

Application to Physics: The Centripetal ForceFc = centripetal forcer= radiusv = speed of objectm = mass of objectFc= (m v2)/rAccording to this equation, what is the

relationship between?i)Force and massii) Force and speed of objectiii) Force and radius of circular motion

Application to Physics: The Gravitational Force

Linear or Non-Linear?

a)Gravitational Force and massb) Gravitational force and radial distance between the masses

Practice calculating slope of a line

12

12

xx

yym

The slope of a line measures its steepness.

The formula we use to calculate slope is slope = rise/run

Practice Problem 1: Find the slope

This line goes through both of these points,(6,0) and (9,2)

Slope = ???

Practice Problem 2: Find the slope

Slope = ???

Practice Problem 3:Find the slope of a line that goes through

points(4,7) and (2,11)

Write the equation of this line.