To graph the equation y = (1/3)|x| - 2, you need to substitute different integer values of x from -3 to 3 to find their respective y-values.
Let's start by choosing a value for x and then calculate the corresponding y-value:
For x = -3:
Substituting x = -3 into the equation: y = (1/3)|-3| - 2
Simplifying: y = (1/3)(3) - 2
Calculating: y = 1 - 2
Result: y = -1
For x = -2:
Substituting x = -2 into the equation: y = (1/3)|-2| - 2
Simplifying: y = (1/3)(2) - 2
Calculating: y = 2/3 - 2
Result: y ≈ -1.33
Continuing this process for the remaining values of x, we get:
x = -1: y ≈ -0.67
x = 0: y = -2
x = 1: y ≈ -1.67
x = 2: y ≈ -1.33
x = 3: y ≈ -1
Now that we have the corresponding y-values, we can plot the points on a graph with the x-values (-3, -2, -1, 0, 1, 2, 3) on the x-axis and the y-values (-1, -1.33, -0.67, -2, -1.67, -1.33, -1) on the y-axis.
Using these 7 points, you can plot them and visualize the graph. Remember that for negative values of x, you need to flip the y-values to maintain the absolute value property.
The resulting graph will have a shape similar to a V, with the vertex at (0, -2). The left branch of the V will touch the x-axis at (-3, -1), and the right branch will touch the x-axis at (3, -1).
I hope this explanation helps you understand how to graph the given equation.