2.5 and 2.62.5 and 2.6Linear and Non-Linear and Non-Linear RelationsLinear Relations

Linear RelationLinear Relation

• Two variables form a Two variables form a straight linestraight line when when graphed.graphed.(meaning the variables change at a (meaning the variables change at a constantconstant rate) rate)

• A line of best fit can be used to represent A line of best fit can be used to represent the data. the data.

Non-Linear RelationsNon-Linear Relations

• Two variables do not form a straight line Two variables do not form a straight line when graphed (one variable does not when graphed (one variable does not change at a constant rate in relation to change at a constant rate in relation to another).another).

• A curve of best fit can be used to A curve of best fit can be used to represent the data. represent the data.

PracticePractice

• On your worksheet draw your curves On your worksheet draw your curves and lines of best fit. and lines of best fit.

Distance vs Time GraphDistance vs Time Graph

• A common type of graph is a A common type of graph is a Distance-Time Distance-Time graph which shows graph which shows what happens to the distance what happens to the distance variable (y) as the time variable (x) variable (y) as the time variable (x) changes . changes .

• These types of graphs can be These types of graphs can be Linear Linear or or Non-LinearNon-Linear..

For the following distance-time graph provide For the following distance-time graph provide a possible explanation for what is occurring in a possible explanation for what is occurring in

each section.each section.

Lets look at the graphLets look at the graph• 1st Section:-Starts running away from home (25 1st Section:-Starts running away from home (25

sec)sec)• 2nd Section: stops moving (out of breath)2nd Section: stops moving (out of breath)• 3rd Section: starts to head home (5 sec)3rd Section: starts to head home (5 sec)• 4th section: Stops to get breath back…4th section: Stops to get breath back…• 5th Section: Gentle jog back home5th Section: Gentle jog back home• 6th Section: Gentle jog away but increases speed 6th Section: Gentle jog away but increases speed

at endat end• 7th Section: Heads back home at constant speed.7th Section: Heads back home at constant speed.• Find the speed at which the object or person was Find the speed at which the object or person was

moving for the last section: moving for the last section: – Goes 40 meters in 20 secondsGoes 40 meters in 20 seconds= = 40m40m 20s20s=2m/s =2m/s

• HW. p. 83 #1, 3, 5, 7HW. p. 83 #1, 3, 5, 7• p. 91 #1bcd, 3, 4, 7, 8p. 91 #1bcd, 3, 4, 7, 8