Exercise 9 Page 588

Practice makes perfect

a The slope

m

tells us how steep the line is. The

y -

b

shows where the line cuts the

y -

axis. Examining the line of best fit, we can identify these values.

y = 0.229 + 0.738 x

A slope of

0.738

means that for every extra ounce of meat we buy, the price increases on average by

$ 0.738 .

The

y -

intercept of

0.229

tells us that if we buy

0

ounces of meat, the cost is

$ 0.229 .

However, this does not make sense, since then we would be paying even if we did not buy anything.

b The residual is the actual value minus the predicted value.

Residual = Actual value - Predicted value

From the exercise, we know that the actual value when buying

3

oz. of meat is

$ 3.20 .

To calculate the predicted value, we have to substitute

x = 3

into the line of best fit.

y = 0.229 + 0.738 x

$x = 3$

y = 0.229 + 0.738 (3)

y = 0.229 + 2.214

Add terms

y = 2.443

Having calculated the predicted value, we can find the residual.

Residual = 3.2 - 2.443 = 0.757

Since the residual is positive, the model understates the cost at this level.

c One pound equals

16

ounces. If the price is reasonable, the model from Part A should give a price that is roughly around

$ 14.70

when substituting

16

for

x .

y = 0.229 + 0.738 x

$x = 16$

y = 0.229 + 0.738 (16)

y = 0.229 + 11.808

Add terms

y = 12.037

The price is a bit too high to be reasonable.

11.1.1 Introduction to Constructions p.587-589

11.1.2 Constructing Bisectors p.592-593

11.1.3 More Explorations with Constructions p.597-599

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