...

# Solutions

## Activities 1

### 1.1)

a)

 $x$-values $0$ $1$ $2$ $3$ $4$ $5$ $6$ $y$-values $5$ $6$ $7$ $8$ $9$ $10$ $11$

b)

 $x$-values $0$ $1$ $2$ $3$ $4$ $5$ $6$ $y$-values $1$ $4$ $7$ $10$ $13$ $16$ $19$

c)

 $x$-values $0$ $1$ $2$ $3$ $4$ $5$ $6$ $y$-values $8$ $6$ $4$ $2$ $0$ $-2$ $-4$

d)

 $x$-values $0$ $1$ $2$ $3$ $4$ $5$ $6$ $y$-values $-4$ $6$ $16$ $26$ $36$ $46$ $56$

### 1.2)

a)

 $x$-values $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $y$-values $-6$ $-4$ $-2$ $0$ $2$ $4$ $6$

b)

 $x$-values $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $y$-values $13$ $12$ $11$ $10$ $9$ $8$ $7$

c)

 $x$-values $y$-values -3 -17 -2 -13 -1 -9 0 -5 1 -1 2 3 3 7
 $x$-values $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $y$-values $-17$ $-13$ $-9$ $-5$ $-1$ $3$ $7$

d)

 $x$-values $y$-values -3 -20 -2 -12 -1 -4 0 4 1 12 2 20 3 28
 $x$-values $-3$ $-2$ $-1$ $0$ $1$ $2$ $3$ $y$-values $-20$ $-12$ $-4$ $4$ $12$ $20$ $28$

## Activities 2

### 2.1)

a)
$a=2$, $b=1$, $f\left(x\right)=2x+1$
b)
$a=2$, $b=0$, $f\left(x\right)=2x$
c)
$a=3$, $b=3$, $f\left(x\right)=3x+3$
d)
$a=1$, $b=10$, $f\left(x\right)=x+10$

### 2.2)

a)
$a=2$, $b=10$, $f\left(x\right)=2x+10$
b)
$a=-4$, $b=10$, $f\left(x\right)=-4x+10$
c)
$a=-3$, $b=9$, $f\left(x\right)=-3x+9$
d)
$a=-1$, $b=32$, $f\left(x\right)=-x+32$

## Activities 3

### 3.1)

a)
$y=4x+2$
b)
$y=3x-2$
c)
$y=-2x+3$
d)
$y=-x-4$

a)
$y=4x+2$
b)
$y=3x-2$
c)
$y=-2x+3$
d)
$y=-x-4$

### 3.2)

a)
$y=1.5x+3$
b)
$y=-2x+3.5$
c)
$y=3.5x+1$
d)
$y=-3x+0.5$

a)
$y=1.5x+3$
b)
$y=-2x+3.5$
c)
$y=3.5x+1$
d)
$y=-3x+0.5$

## Activities 4

### 4.1)

$f\left(x\right)$ and $h\left(x\right)$

### 4.2)

Only (b) is proportional, $y=4x$

### 4.3)

Graph (a) is a proportional function, $f\left(x\right)=5x$

## Activities 5

### 5.1)

$p\left(x\right)$ $\left(k=1000\right)$ and $h\left(x\right)$ $\phantom{\rule{-0.17em}{0ex}}\left(k=\frac{1}{3}\right)$

### 5.2)

Tables a) and d) are inversely proportional

### 5.3)

All the graphs except (c) are inversely proportional

## Activities 6

### 6.1)

You choose Taxi King. Then you pay \$$25$ for the trip, while City Taxi would have costed \$$40$.

### 6.2)

a)
\$$420$
b)
21 friends went on the trip.

a)
\$$420$
b)
21 friends went on the trip.