Chapter 4.2, Problem 4.28E

(a)

To determine

To show that the equation of the least square is $y=10-\frac{2}{3}x$ using the graph and some algebra.

Explanation of Solution

The equation is of the form $y=ax+b$ with $a$ the slope and the $b$

  $y$ -intercept.

The $y$ -intercept is $10$ and thus $b=10$ .

We note that $(3,8)$ is a point on the line:

  $8=a(3)+10$

Subtract $10$ from each side:

  $-2=3a$

Thus, $a=-\frac{2}{3}$

Thus the equation then becomes:

  $y=10-\frac{2}{3}x$

(b)

To determine

To find out the slope of the line and explain what is this setting.

Answer to Problem 4.28E

The slope of the coefficient is $-\frac{2}{3}$ .

Explanation of Solution

The slope of the coefficientis $-\frac{2}{3}$ .

This means that if three more pizzas were eaten, then about two laps less were run.

(c)

To determine

To find out the $y$ -intercept of the line and explain what is this setting.

Answer to Problem 4.28E

The $y$ -intercept is the constant of the equation i.e. $10$ .

Explanation of Solution

The $y$ -intercept is the constant of the equation i.e. $10$ .

This means that if no pizza slices were consumed, then about $10$ laps were run.