Question

4.2 3. complete each table of values.
a) $y = x + 1$\
\

$x$	$y$	\
---	---	\
1	\underline{2}	\
2	\underline{3}	\
3	\underline{4}	\
4	\underline{5}	\

\
b) $y = x - 1$\
\

$x$	$y$	\
---	---	\
2	\underline{1}	\
4	\underline{3}	\
6	\underline{5}	\
8	\underline{7}	\

\

1. on his first birthday, hayden was given $20 by his grandfather. each years gift is $10 more than the year before. the data is given in the table below\

\
grandfather’s gifts\
\

birthday, $n$	gift, $g$ ($)	\
---	---	\
1	20	\
2	30	\
3	40	\
4	50	\

\
a) graph the data.\
b) is the graph linear? explain your thinking.\
the points \underline{make a straight line}, so the graph is \underline{linear}.\
c) should the points be joined? explain why or why not.\
\
\
\
d) how are the patterns in the table shown in the graph? in the table,\
as the birthday increases by \underline{1}, the gift value increases by \underline{10}. each point\
on the graph is \underline{across} and \underline{1 higher} from the previous point.\
\
4.3 5. write an equation to describe each line.\
a) \
\
(graph with x from -4 to 4, y from -4 to 4, origin at (0,0))\
\
\underline{$y = 4x - 4$}\
b) \
\
(graph with x from -6 to 6, y from -6 to 6, origin at (0,0))\
\
\underline{$y = 6x - 6$}\
c) \
\
(graph with x from -10 to 10, y from -10 to 10, origin at (0,0))\
\
\underline{$y = 10x - 10$}

Explanation:

Step1: Verify 4a (already done)

The graph plots points (1,20), (2,30), (3,40), (4,50) correctly, matching the table.

Step2: Verify 4b (already done)

Linear graphs form straight lines; the points lie on a straight line, so it is linear.

Step3: Answer 4c

Birthdays are whole numbers (discrete data). We only have gift values for specific birthdays, not every value between them.

Step4: Verify 4d (correct values)

In the table, $n$ increases by 1, $g$ increases by 10. On the graph, each point is 1 unit right and 10 units up from the prior point.

Step5: Correct 5a equation

The line passes through (0,0) (origin), slope $m=\frac{4}{4}=1$. Equation: $y=x$.

Step6: Correct 5b equation

The line passes through (0,0), slope $m=\frac{6}{6}=1$. Equation: $y=x$.

Step7: Correct 5c equation

The line passes through (0,0), slope $m=\frac{10}{10}=1$. Equation: $y=x$.

Answer:

Question 3 (already completed correctly):

a) For $y=x+1$:
$x=1, y=2$; $x=2, y=3$; $x=3, y=4$; $x=4, y=5$
b) For $y=x-1$:
$x=2, y=1$; $x=4, y=3$; $x=6, y=5$; $x=8, y=7$

Question 4:

a) (Graph is already correctly plotted with points (1,20), (2,30), (3,40), (4,50))
b) Yes, the graph is linear. The plotted points lie on a single straight line.
c) No, the points should not be joined. Birthdays are discrete (whole-number values only), so there is no valid gift amount for values between the listed birthdays.
d) In the table, as the birthday increases by $\boldsymbol{1}$, the gift value increases by $\boldsymbol{10}$. Each point on the graph is $\boldsymbol{1\ \text{unit to the right}}$ and $\boldsymbol{10\ \text{units up}}$ from the previous point.

Question 5:

a) $y=x$
b) $y=x$
c) $y=x$