Question

toby is preparing to sell some wooden blocks at a garage sale. before pricing individual bags of blocks, he decides to determine the approximate number of blocks per pound by researching the weights of different sets of blocks. the graph shows his data. graph: toy block research, x - axis: weight of set (lb), y - axis: number of blocks based from the graph, how many blocks are in each pound? round to the nearest block. options: 10, 20, 30, 40

Explanation:

Step1: Analyze the graph's slope (rate)

The graph shows a linear relationship between the number of blocks and the weight of the set (in pounds). To find the number of blocks per pound, we can calculate the slope of the line. Let's take two points, e.g., when weight \( x = 1 \) lb, number of blocks \( y = 30 \) (approx from the graph), and when \( x = 2 \) lb, \( y = 60 \) (approx). The slope \( m=\frac{\Delta y}{\Delta x}=\frac{60 - 30}{2 - 1}=\frac{30}{1} = 30\)? Wait, no, wait. Wait, maybe better to take the origin? Wait, the line passes through (0,0) and let's see another point. Let's check when weight is 1 lb, how many blocks? From the graph, when x=1, y=30? Wait, no, maybe I misread. Wait, the y - axis is number of blocks, x - axis is weight in lb. Let's take a point: when x = 1, y = 30? Wait, no, let's check the slope. Let's take two clear points. Suppose at x = 2 lb, number of blocks is 60? Wait, no, maybe the slope is calculated as number of blocks per pound. Let's see, if we take the line, the slope (rate) is number of blocks / weight. Let's take a point where weight is 1 lb, number of blocks is 30? Wait, no, maybe the correct way: the line is linear, so the equation is \( y = mx \), where \( y \) is number of blocks, \( x \) is weight in lb, and \( m \) is blocks per pound. Let's take a point, say when \( x = 2 \), \( y = 60 \) (from the graph, maybe). Then \( m=\frac{y}{x}=\frac{60}{2}=30 \)? Wait, no, wait the options are 10,20,30,40. Wait, maybe another point. Let's take x = 1, y = 30? No, maybe x = 1, y = 30? Wait, no, let's check the graph again. Wait, the y - axis starts at 15, 20, 30, 45, 60, 75, 90, 105, 120? Wait, no, the y - axis labels: 15, 30, 45, 60, 75, 90, 105, 120? Wait, the first mark after 0 is 15, then 30, etc. Wait, when x = 1 (weight 1 lb), the number of blocks is 30? No, maybe x = 1, y = 30? Wait, no, let's calculate the slope. Let's take two points: (0,0) and (2,60). Then slope \( m=\frac{60 - 0}{2 - 0}=30 \). So the number of blocks per pound is 30. Wait, but let's check another point. If x = 3, y = 90, then \( \frac{90}{3}=30 \). So the rate is 30 blocks per pound.

Answer:

30 (corresponding to the option with 30, e.g., if the options are A.10, B.20, C.30, D.40, then C. 30)