model each rule with a table of values and a graph..

f(x) = 1.5x -3

Make a T-chart with x and f(x). Pick several x values, like -2, -1, 0, 1, and 2. Plug those into your equation to get f(x) for each. Then plot the points and connect the dots.

Hi, sorry I am not good with math, so can you explain it more please.

Sure! To model the rule f(x) = 1.5x - 3 with a table of values and a graph, we can select various values for x, calculate the corresponding values for f(x), and then represent them in both table and graph formats.

Table of Values:
Let's choose some values for x, calculate f(x) using the given rule, and construct a table:

| x | f(x) |
|:-----:|:-------:|
| -2 | -6 |
| -1 | -4.5 |
| 0 | -3 |
| 1 | -1.5 |
| 2 | 0 |
| 3 | 1.5 |

Graph:
Similarly, we can plot the values from the table on a graph:

^
|
| . (3, 1.5)
| /
| /
| /
| /
| /
| . (2, 0)
| /
| /
| / (1, -1.5)
|/
| (0, -3)
|-------------------------------> x
| /
| /
| /
| /
| /
| /
| . (-1, -4.5)
|/
|------------- (-2, -6)

On the graph, each point represents a value from the table. By connecting these points with a straight line, we can visualize the linear relationship described by the function f(x) = 1.5x - 3.

To model the rule f(x) = 1.5x - 3 with a table of values and a graph, you can follow these steps:

1. Create a table of values: Choose a few values for x, and substitute them into the given rule to find the corresponding values for f(x).

Let's choose some values for x:

x | f(x)
---------------
-3 |
-2 |
-1 |
0 |
1 |
2 |
3 |

To find the corresponding values for f(x), substitute each x value into the rule f(x) = 1.5x - 3. For example, when x=-3, f(x) = 1.5(-3) - 3 = -6.5. Fill out the rest of the table using this method.

x | f(x)
---------------
-3 | -6.5
-2 | -6
-1 | -4.5
0 | -3
1 | -1.5
2 | 0
3 | 1.5

2. Create a graph: Plot the ordered pairs from the table of values on a set of axes.

On the x-axis, mark the values of x that we chose: -3, -2, -1, 0, 1, 2, and 3.
On the y-axis, mark the corresponding values of f(x) that we found: -6.5, -6, -4.5, -3, -1.5, 0, and 1.5.

Plot these points on the graph and draw a line through them to represent the function.

The resulting graph will be a straight line with a positive slope of 1.5 that crosses the y-axis at -3.

Note: If you're using software or a graphing calculator, you can plot the points and draw the graph more accurately.