Question

the local animal shelter showed commercials about adopting pets on one of the local television stations. the scatter plot below shows the number of pet adoptions and the number of commercials aired over a one - week period.

scatter plot titled pet - a - thon with x - axis number of commercials and y - axis number of pet adoptions, and a trend line

based on the trend line, which is the expected number of adoptions if seven commercials aired?

a. 40
b. 50
c. 55
d. 60

Explanation:

Step1: Analyze the trend line

The trend line (dashed line) in the scatter plot shows a linear relationship. Let's observe the pattern: when the number of commercials (x) increases, the number of adoptions (y) increases.

Step2: Estimate for x=7

Looking at the trend line, we can see the slope and the pattern. For example, when x=1, y≈10; x=2, y≈20; x=3, y≈25; x=4, y≈35; x=5, y≈38; x=6, y≈50? Wait, no, let's check the grid. Wait, the y-axis is number of pet adoptions, x-axis number of commercials. Let's see the trend line: when x=1, y≈10; x=2, y≈20; x=3, y≈25? No, maybe better to see the pattern. Wait, the options are 40,50,55,60. Wait, when x=6, the trend line is around 50? Wait, no, the scatter plot: let's see the trend line. Let's assume the trend line has a slope. Let's take two points on the trend line. For example, when x=1, y=10; x=2, y=20 (so slope 10). Wait, no, maybe x=1, y=10; x=2, y=20; x=3, y=30? Wait, no, the dots: when x=1, the dot is at y=10; x=2, y=22; x=3, y=24; x=4, y=38; x=5, y=38; x=6, y=50; x=7, what? Wait, the trend line: let's see, the dashed line. Let's check the y-values as x increases. When x=7, following the trend line, which is a straight line. Let's see the slope: from x=1 (y=10) to x=6 (y=50), the slope is (50-10)/(6-1)=40/5=8? No, maybe my initial points are wrong. Wait, the graph: the y-axis has marks at 5,10,15,20,25,30,35,40,45,50,55,60. The x-axis at 1,2,3,4,5,6,7,8. The trend line: when x=1, y=10; x=2, y=20; x=3, y=30? No, the dot at x=2 is around y=22, x=3 around y=24, but the trend line is dashed. Wait, maybe the trend line is linear, and we can see that for x=6, the trend line is at y=50? No, wait the option B is 50, C 55, D 60. Wait, maybe when x=7, the trend line is at 55? Wait, no, let's look again. Wait, the problem is: based on the trend line, expected number of adoptions when 7 commercials are aired. Let's see the trend line: when x=6, the trend line is at y=50? No, the dot at x=6 is around 50, and the trend line is through the middle. Wait, maybe the trend line at x=7 is 55? Wait, no, let's check the options. Wait, the correct answer is B? No, wait maybe I made a mistake. Wait, let's see the scatter plot: the trend line (dashed) goes through the points. Let's take x=1, y=10; x=2, y=20; x=3, y=30; x=4, y=40; x=5, y=40; x=6, y=50; x=7, y=60? No, that can't be. Wait, the options: A.40, B.50, C.55, D.60. Wait, maybe when x=7, the trend line is at 55? Wait, no, let's look at the graph again. Wait, the y-axis: each grid line is 5? Wait, 5,10,15,20,25,30,35,40,45,50,55,60. So from x=1 (y=10) to x=6 (y=50), that's 5 units in x, 40 in y, slope 8. So at x=7, y=10 + 8*(7-1)=10+48=58, close to 55? Wait, maybe the trend line is a bit different. Alternatively, look at the scatter plot: when x=6, the trend line is at y=50, x=7, it should be 55? Wait, the option C is 55, D 60. Wait, maybe the correct answer is B? No, I think I messed up. Wait, let's check the original problem again. The scatter plot: the trend line (dashed) – let's see the points. At x=1, y=10; x=2, y=20; x=3, y=30; x=4, y=40; x=5, y=40; x=6, y=50; x=7, y=60? No, that's slope 10. Then at x=7, y=10 + 10*(7-1)=70, which is not an option. Wait, maybe the y-axis is not 10 per x. Wait, the y-axis: the first mark is 5, then 10,15,20,25,30,35,40,45,50,55,60. So each grid line is 5. So when x=1, y=10 (second line); x=2, y=20 (fourth line); x=3, y=25 (fifth line? No, 5,10,15,20,25,30,35,40,45,50,55,60. So 5 is first, 10 second, 15 third, 20 fourth, 25 fifth, 30 sixth, 35 seventh, 40 eighth, 45 ninth, 50 tenth, 55 eleventh, 60 twelfth. So the dot at x=1 is at y=10 (second line), x=2 at y=20 (fourth line), x=3 at y=25 (fifth line), x=4 at y=35 (seventh line), x=5 at y=38 (between seventh and eighth), x=6 at y=50 (tenth line), x=7 – following the trend line, which is a straight line. From x=1 (y=10) to x=6 (y=50), the change in x is 5, change in y is 40, so slope 8. So at x=7, y=10 + 8*6=58, which is close to 55 (option C) or 60 (option D). Wait, maybe the trend line is a bit steeper. Alternatively, look at the options: the correct answer is B? No, I think I made a mistake. Wait, the problem is from a scatter plot, and we need to estimate the y-value when x=7. Looking at the trend line, when x=6, the trend line is at y=50, so x=7 should be 50 + 5? No, maybe the trend line has a slope of 10. Wait, x=1:10, x=2:20, x=3:30, x=4:40, x=5:40, x=6:50, x=7:60? But 60 is option D. But the dot at x=6 is at 50, and the trend line is through the middle. Wait, maybe the answer is B.50? No, I'm confused. Wait, let's check the options again. The options are A.40, B.50, C.55, D.60. Looking at the trend line, when x=7, the expected number is 50? No, maybe 55. Wait, I think the correct answer is B.50? No, I'm not sure. Wait, maybe the trend line is linear, and we can calculate the equation. Let's take two points on the trend line: (1,10) and (6,50). The slope is (50-10)/(6-1)=40/5=8. So the equation is y=8x + 2. Wait, when x=1, 8*1+2=10, correct. When x=7, y=8*7 + 2=58, which is close to 55 or 60. But the options have 55 (C) and 60 (D). Wait, maybe my points are wrong. Let's take (2,20) and (6,50). Slope (50-20)/(6-2)=30/4=7.5. Equation: y=7.5x + 5. When x=7, y=7.5*7 +5=52.5+5=57.5, close to 55 or 60. So the closest is 55 (C) or 60 (D). Wait, maybe the trend line at x=7 is 55. So the answer is C.55? No, maybe B.50. Wait, I think I need to look at the graph again. The scatter plot: the trend line (dashed) – when x=6, the trend line is at 50, so x=7 should be 50 + 5=55? Yes, that makes sense. So the expected number is 55.

Answer:

C. 55