write and graph the inverse variation when y=3 and x=2 find k =
write the inverse variation
fill in the table of values and graph
x = -3 ,-2 ,-1,1,2,3
y= ?
since you have no values for y, you cannot determine k.
To write the inverse variation equation, we'll use the formula: y = k/x, where k is a constant. Given that y = 3 when x = 2, we can substitute these values into the equation and solve for k.
3 = k/2
To find k, we can multiply both sides of the equation by 2:
3 * 2 = k
6 = k
So, k = 6.
Now we can write the inverse variation equation as y = 6/x.
To fill in the table of values for y, we substitute the given x-values into the inverse variation equation and compute the corresponding y-values:
For x = -3:
y = 6/(-3) = -2
For x = -2:
y = 6/(-2) = -3
For x = -1:
y = 6/(-1) = -6
For x = 1:
y = 6/1 = 6
For x = 2:
y = 6/2 = 3
For x = 3:
y = 6/3 = 2
Now we can create a table of values:
x | y
--------------
-3 | -2
-2 | -3
-1 | -6
1 | 6
2 | 3
3 | 2
To graph the inverse variation, we plot the points from the table on a coordinate plane, where the x-values represent the horizontal axis and the y-values represent the vertical axis. Connecting these points with a smooth curve will give us the graph of the inverse variation equation.
Here is the graph of the inverse variation equation y = 6/x:
|
6 | *
| *
| *
| *
| *
|*
+---------------------
-3 -2 -1 1 2 3
Note: The graph is a hyperbola, where the curve approaches the x-axis but never touches it. The line of symmetry is the y-axis (x = 0).