Explanation:
To graph the relationship between the number of pencils and the number of boxes, we can plot some points that satisfy the equation p = 144b.
We can choose any values of b and calculate the corresponding values of p using the equation. For example:
When b = 0, p = 144(0) = 0. So one point on the graph is (0, 0).
When b = 1, p = 144(1) = 144. So another point on the graph is (1, 144).
When b = 2, p = 144(2) = 288. So another point on the graph is (2, 288).
We can continue this process to find more points, or we can notice that the equation p = 144b represents a linear relationship between p and b with a slope of 144. This means that every time we increase b by 1, we increase p by 144.
We can use this information to graph the equation by starting at the y-intercept (0, 0) and then moving up 144 units for each unit we move to the right. This gives us a straight line with a slope of 144 passing through the origin.
The graph of the equation p = 144b looks like this:
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0 1 2 3 4 b
The horizontal axis represents the number of boxes (b), and the vertical axis represents the number of pencils (p). Each dot on the graph represents a point that satisfies the equation p = 144b.