Janet is training for a marathon. She decides to track her time per mile, in minutes, for 8 weeks. Which equation best fits the data?
A graph is labeled as Marathon Training. The horizontal axis is labeled as Weeks and the vertical axis is labeled as Time per mile left parenthesis minutes right parenthesis. The values on the horizontal axis range from 0 to 10 in increments of 2 and the values on the vertical axis range from 0 to 10 in increments of 2. Nine points are marked on the graph with their coordinates approximately equal to (0, 10), (1, 9 decimal point 9), (2, 9 decimal point 6), (3, 9 decimal point 5), (4, 9 decimal point 4), (5, 9 decimal point 2), (6, 9), (7, 8 decimal point 7), and (8, 8 decimal point 6).
A.y=0.18x + 10.06
B.y=−0.18x + 10.06
C.y = 2x + 8.6
D.y = −2x + 8.6
I THINK ITS C AM I RIGHT
slope: (taking last two points); (yf-yi)/(xf-xi)= (8.6-10)/(8-0)=-1.4/8=-.18
intercept:
y=-.18x+ b using the point 0,10 then b=10
Janet takes 12 minutes to run around the track one time and george takes 8 minutes to run around the track. In how many minutes will they both be at the starting of the track at the same time?
To determine which equation best fits the data, we need to analyze the given points and see which equation matches the trend.
Let's plot the given points on the graph:
(0, 10)
(1, 9.9)
(2, 9.6)
(3, 9.5)
(4, 9.4)
(5, 9.2)
(6, 9)
(7, 8.7)
(8, 8.6)
When examining the points, we can observe that the time per mile decreases as the number of weeks (x-axis) increases. This suggests a negative correlation between the two variables.
Now, let's analyze the four given equations:
A. y = 0.18x + 10.06
B. y = -0.18x + 10.06
C. y = 2x + 8.6
D. y = -2x + 8.6
Since we established that there is a negative correlation (as x increases, y decreases), we can exclude options A and C, which both have positive slopes.
Now, let's compare options B and D:
B. y = -0.18x + 10.06
D. y = -2x + 8.6
To determine which equation fits the data, let's examine the given points. The data points show a consistent decrease in y as x increases. This suggests that the slope is relatively steep.
If we compare the values of 0.18 (option B) and 2 (option D), 2 is a larger value, indicating a steeper negative slope. Therefore, option D (y = -2x + 8.6) is the equation that best fits the given data.
Hence, your initial guess was incorrect, and the correct answer is option D.