linear interpolation the power of prediction!. scenario 1: birthday cakes you had a birthday cake...

Linear InterpolationThe Power of Prediction!

Scenario 1: Birthday Cakes• You had a birthday cake sitting on your

kitchen table. Your cousin came over. When you came back into the kitchen, part of the birthday cake was gone and your cousin had frosting on his face.

• What happened?

We ASSUME (predict):• That your cousin ate the birthday cake!• But do we know for 100% certainty?• No! But, it’s a pretty good guess.

We ASSUME (predict):• Hypothesize, guess, predict.• These are all synonyms.

How does this relate to our grass?

There are 2 math words for prediction: Interpolate and Extrapolate.

Interpolate: • Predicting within the data (like with your

cousin and the birthday cake).• Predicting what has already happened.• GRASS: Predicting how tall your grass

was on Sunday when we were not here.

Extrapolate:• Predicting what will happen.• Predicting outside the data.• Predicting how tall your grass could grow

given NO LIMITING FACTORS.

How do we do this?• We use our scatter plots (graphs)!

How tall was my grass on day 7?

1: Find points on either side….

2: find the slope.

2: find the slope.

2: find the slope.

2: find the slope.

We found the slope!• The slope between the two known days is ½. • So what is the height (y value) at day 7?• Plug it back in!

Take slope and one (x, y)

Take slope and one (x, y)

And plug into y = mx + b

And plug into y = mx + b

And plug into y = mx + b

And plug into y = mx + b

And plug into y = mx + b

And plug into y = mx + b

The y-intercept b = -2 ??• Yes! • But our grass was never -2 inches tall!• We are basing our calculation on just

when the grass was growing. • Based on that information, math will give

us a negative y-intercept.• This is where life and math clash (not

the only time!)

Our equation then is….

Our equation then is….

Our equation then is….

And day 7’s height is...

And day 7’s height is...

This is an exact answer.

• We can also read the graph to get an approximate answer.

We just interpolated!• We figured out how tall our grass may

have been on day 7!• We can also use our y = mx + b formula

to predict into the future!

IMPORTANT!• As grass growth slows, your “line of fit”

(your equation) will change. • Why?• How?

Classwork:1: Find the slope of the line formed between

your day 5 and day 8.2: plug your slope and one of the two points

back into y = mx + b to find b.3: Construct YOUR graph’s y = mx + b

formula to predict day 7.