Question

tai surveyed his classmates about the number and types of pets they owned, and the number of missing assignments in the class and their grade in the class. he created the two scatterplots shown below. use the scatterplots to answer questions 4-7.
graph a
graph b
4 what is the y-intercept of the trend line of graph b?
5 based on graph b, what grade would someone with 3 missing assignments have?
a 60
b 40
c 80
d 30
6 which statement below accurately describes graph a?
a the more dogs a student has, the more cats they have.
b students have twice as many dogs as cats.
c students with more than five dogs have more than five cats.
d there is no relationship between the number of cats and dogs a student owns.
7 after how many missing assignments will a student likely have a zero for an average?
a 5
b 6
c 7
d 9

Explanation:

Question 4

Step1: Recall y-intercept definition

The y-intercept is the value of \( y \) when \( x = 0 \) on the trend line. For Graph B, the x - axis is "Number of Missing Assignments" and y - axis is "Average Grade".

Step2: Analyze Graph B's trend

Looking at the scatterplot, the trend line (if we were to draw it) would intersect the y - axis (when number of missing assignments \( x = 0 \)) at a value. From the pattern of the points (as \( x \) increases, \( y \) decreases), when \( x = 0 \), we can estimate the y - intercept. By looking at the slope and the points, when \( x = 0 \), the y - intercept should be around 100? Wait, no, looking at the graph, the first point when \( x = 1 \) is around 90, \( x = 2 \) around 80, so the slope is \( \frac{80 - 90}{2 - 1}=- 10 \). Using the point - slope form \( y - y_1=m(x - x_1) \), taking \( (1,90) \), \( y-90=-10(x - 1) \). When \( x = 0 \), \( y-90=-10(-1)\Rightarrow y = 100 \)? Wait, maybe my initial estimation is wrong. Wait the graph's y - axis for Graph B: the top is 90, 80, etc. Wait, maybe the y - intercept is 100? Wait, no, let's check the grid. The y - axis of Graph B: the first grid line above 90? Wait, maybe the y - intercept is 100. Wait, but maybe the correct way is to see that when \( x = 0 \), the trend line would pass through \( y = 100 \). But maybe the answer is 100? Wait, maybe I made a mistake. Wait, let's re - examine. The x - axis is number of missing assignments (x), y - axis is average grade (y). The points are (1,90), (2,80), (3,70), (4,50? No, (4,40), (5,25), (6,15), (7,10). Wait, no, the points: when x = 1, y≈90; x = 2, y≈80; x = 3, y≈70; x = 4, y≈40? No, that can't be. Wait, maybe the points are (1,90), (2,80), (3,70), (4,40) is wrong. Wait, the original graph: Graph B has x from 1 - 9, y from 10 - 90. So the first point (x = 1, y≈90), x = 2, y≈80, x = 3, y≈70, x = 4, y≈40? No, that's inconsistent. Wait, maybe the correct trend is linear with slope - 10. So equation \( y=100 - 10x \). So when x = 0, y = 100. But maybe the answer is 100. Wait, but maybe the graph's y - axis starts at 10, so the y - intercept is 100.

Step1: Locate x = 3 on Graph B

On Graph B, the x - axis is "Number of Missing Assignments" and y - axis is "Average Grade". We need to find the y - value (grade) when \( x = 3 \) (3 missing assignments).

Step2: Analyze the trend or the point

Looking at the scatterplot, when the number of missing assignments \( x = 3 \), the corresponding average grade (y - value) is around 70? Wait, no, the options are 60,40,80,30. Wait, maybe the points: when x = 1, y = 90; x = 2, y = 80; x = 3, y = 70? But 70 is not an option. Wait, the options are A.60, B.40, C.80, D.30. Wait, maybe I misread the graph. Wait, maybe the point for x = 3 is 70, but the closest option? No, maybe the trend line: the equation is \( y=100 - 10x \). When \( x = 3 \), \( y=100 - 30 = 70 \), but 70 is not an option. Wait, maybe the graph's points are (1,90), (2,80), (3,60)? Wait, maybe the correct answer is A.60? Wait, no, let's check the options again. The question is "Based on Graph B, what grade would someone with 3 missing assignments have?". The options are A.60, B.40, C.80, D.30. If we look at the scatterplot, when x = 3 (number of missing assignments), the point is around 70, but maybe the trend line is approximated as \( y = 100-10x \), no. Wait, maybe the graph has a point at x = 3, y = 60? Maybe I made a mistake in the initial analysis. Alternatively, maybe the answer is A.60.

Step1: Analyze each option for Graph A

Graph A has x - axis "Number of Dogs" and y - axis "Number of Cats".

• Option A: "The more dogs a student has, the more cats they have." Looking at the scatterplot, the points are scattered randomly. There is no upward trend as x (dogs) increases. So A is wrong.
• Option B: "Students have twice as many dogs as cats." For example, if a student has 1 dog, the number of cats varies (1,3,8, etc.). So this is not true.
• Option C: "Students with more than five dogs have more than five cats." Looking at the x - axis (dogs), when dogs > 5 (x>5), the number of cats: for x = 6, cats = 0; x = 7, cats = 1,2; x = 9, cats = 0. So this is wrong.
• Option D: "There is no relationship between the number of cats and dogs a student owns." Since the points are scattered without any clear positive or negative trend, this is correct.

Answer:

100 (assuming the trend line equation is \( y = 100-10x \))

Question 5