Questions: Which statements about Jaelyn's data are true? Choose 2 A As indicated by point Y, in twelve minutes of counting there were sixteen grasshoppers spotted. B As indicated by point Z, in twenty-four minutes of observing there were eighteen grasshoppers counted. C As indicated by point X, in six minutes of observing there were eight grasshoppers counted. D Based on the graph, in twenty minutes there were twenty-eight grasshoppers counted. E Based on the graph, in four minutes there were three grasshoppers counted.

Which statements about Jaelyn's data are true? Choose 2 A As indicated by point Y, in twelve minutes of counting there were sixteen grasshoppers spotted. B As indicated by point Z, in twenty-four minutes of observing there were eighteen grasshoppers counted. C As indicated by point X, in six minutes of observing there were eight grasshoppers counted. D Based on the graph, in twenty minutes there were twenty-eight grasshoppers counted. E Based on the graph, in four minutes there were three grasshoppers counted.

Solution

Solution Steps

Step 1: Analyze Point Y

Point Y lies on the intersection of x = 16 and y = 12. This means when x (Minutes Counting) is 16, y (Number of Grasshoppers) is 12. Option A states that in twelve minutes there were sixteen grasshoppers, which is the opposite of what the graph shows. So, option A is incorrect.

Step 2: Analyze Point Z

Point Z lies on the intersection of x = 24 and y = 18. This means when x (Minutes Counting) is 24, y (Number of Grasshoppers) is 18. Option B states that in twenty-four minutes there were eighteen grasshoppers, which matches the graph. So, option B is correct.

Step 3: Analyze Point X

Point X lies at the intersection of x = 8 and y = 6. This means when x (Minutes Counting) is 8, y (Number of Grasshoppers) is 6. Option C states that in six minutes there were eight grasshoppers, which is the opposite of what the graph shows. So, option C is incorrect.

Step 4: Analyze the Graph for 20 minutes

The graph is a straight line. We can find the equation of the line using two points, say (8,6) and (24,18). The slope is given by \( m = \frac{18-6}{24-8} = \frac{12}{16} = \frac{3}{4} \). Using the point-slope form, the equation of the line is \( y - 6 = \frac{3}{4}(x-8) \), which simplifies to \( y = \frac{3}{4}x \). When x = 20, \( y = \frac{3}{4}(20) = 15 \). Option D states that in twenty minutes there were twenty-eight grasshoppers, but the graph shows 15 grasshoppers. So, option D is incorrect.

Step 5: Analyze the graph for 4 minutes

Using the equation \( y = \frac{3}{4}x \), when x = 4, \( y = \frac{3}{4}(4) = 3 \). Option E states that in four minutes, there were three grasshoppers. This matches the equation of the line. So, option E is correct.

Final Answer

\\(\boxed{B, E}\\)

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