The data in the table illustrate a linear function. Find the slope of the linear function and graph the linear function.

x -3 0 3 6

y -6 -2 2 6

1 answer

To find the slope of the linear function, we use the formula:

slope = (change in y)/(change in x)

If we choose any two points from the table, we can calculate the change in y and change in x to find the slope. Let's choose (-3,-6) and (0,-2):

slope = (-2 - (-6))/(0 - (-3)) = 4/3

So the slope of the linear function is 4/3.

To graph the linear function, we can use the point-slope form of the equation, which is:

y - y1 = m(x - x1)

where m is the slope and (x1,y1) is any point on the line. Let's use the point (0,-2):

y - (-2) = (4/3)(x - 0)

Simplifying, we get:

y = (4/3)x - 2

Now we can plot this line on a coordinate plane using the slope as the rise over run. We get:

```
|
7 |
|
6 |
|
5 |
|
4 |
|
3 |
|
2 | ●
|
1 |
|
0 | ●
|_________
-3 0 3 6
```

The dots represent the points from the table, and the line is the graph of the linear function.