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
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.
To find the slope of the linear function, we can use the formula:
slope = (change in y) / (change in x)
Let's calculate the changes in y and x:
Change in y = final y value - initial y value
Change in x = final x value - initial x value
For the given data, the initial values are (x=-3, y=-6), and the final values are (x=6, y=6).
Change in y = 6 - (-6) = 12
Change in x = 6 - (-3) = 9
Now, we can calculate the slope:
slope = (change in y) / (change in x) = 12 / 9 = 4/3
Therefore, the slope of the linear function is 4/3.
To graph the linear function, we can plot the given points (x, y) on a graph:
( -3, -6 )
( 0, -2 )
( 3, 2 )
( 6, 6 )
Connecting these points, we get a straight line that represents the linear function.