Exercise 38 Page 176

a When we draw an imaginary line through these points it will cut the

x -

axis between

0

and

2

and again cut the

y -

axis at a point below the

x -

axis. Therefore, it appears to have a negative

y -

b The first point is at

x = 4

and its vertical distance from

x -

axis is quite close to

2 .

We can approximate it to be

1.8,

giving us the coordinates

(4, 1.8)

. Following a similar reasoning, the second point is on

(8, 4)

. Let's find the slope of the line that passes through them.

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

Substitute $(8, 4)$ & $(4, 1.8)$

m = \frac{4 - 1 . 8}{8 - 4}

▼

Simplify right-hand side

Subtract terms

m = \frac{2 . 2}{4}

$\frac{a}{b} = \frac{a \cdot 1 0}{b \cdot 1 0}$

m = \frac{2 2}{4 0}

$\frac{a}{b} = \frac{a / 2}{b / 2}$

m = \frac{1 1}{2 0}

A slope of

\frac{1 1}{2 0}

means if we take

20

steps to the right, the graph increases by

11

steps. Conversely, if we take

20

steps to the left, we would have to go down by

11

steps to get to another point.

Communicate Your Answer p.171

Monitoring Progress p.172-174

Exercises p.175-176