Question

How do I draw table to show the amounts invested for each year ? How do I use the table to construct a line graph representing this data ? Between two years was there the largest increase in the investment ? How do I state the value of this increase in investment ?

Answer 1

Using the given histogram which shows the amount invested each year, let's solve for the following:

• (a). Draw a table to show the amounts invested each year.

Using the graph, we have the table:

Year Amount invested ($)

1985 3300

1986 3800

1987 4300

1988 4800

1989 5300

• (b). Let's construct a line graph representing the data.

To construct a line graph, let's create points using the values in the table.

Let x be the number of years after 1985.

We have the points:

(x, y) ==> (0, 3300), (1, 3800), (2, 4300), (3, 4800), (4, 5300)

Plot the points and connect them using a straight line.

• (c). Since the graph is a linear graph, it means it has a constant rate of change.

Therefore, the increase each year is constant.

• (d). The value of increase in investment.

Here, we are to use the slope formula.

Apply the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

Take any two points representing the data:

(x1, y1) ==> (0, 3300)

(x2, y2) ==> (2, 4300)

Plug in the values in the equation and solve for slope, m:

`\begin{gathered} m=(4300-3300)/(2-0) \\ \\ m=(1000)/(2) \\ \\ m=500 \end{gathered}`

The slope is 500.

This means the investment increased constantly by $500 each year.

• ANSWER:

(a). Table:

Year Amount invested ($)

1985 3300

1986 3800

1987 4300

1988 4800

1989 5300

(b). The graph is above.

(c). The increase each year is constant.

(d). The investment increased by $500 each year.