1.The table shows the number of miles driven over time.
Time(hours):4 , 6 , 8 , 10
Distance(miles):204 , 306 , 408 , 510
Express the relationship between distance and time in simplified form as a unit rate. Determine which statement correctly interprets this relationship.
A.51/1; your car travels 51 miles every 1 hour.***
B.204; your car travels 204 miles.
C.1/51; your car travels 51 miles every 1 hour.
D.10; your car travels for 10 hours.
2.What is the slope of the line that passes through the pair of points (2, 5) and (8, 3)?
A.1/3
B.-1/3***
C.3
D.-3
3.What is the slope of the line that passes through the pair of points (3/2, -2) and (-3, 7/3)?
A.-27/26
B.-26/27
C.26/27***
D.27/26
--->*** are my answers, please correct me if I'm wrong I really need help
the answer is 42 miles per hour
Your answers for questions 1 and 2 are correct. However, your answer for question 3 is incorrect.
The correct answer for question 3 is B. -26/27.
To find the slope of a line passing through two points (x1, y1) and (x2, y2), you can use the formula:
slope = (y2 - y1) / (x2 - x1)
Using the given points (3/2, -2) and (-3, 7/3), we have:
slope = (7/3 - (-2)) / (-3 - 3/2)
slope = (7/3 + 6/3) / (-6/2 - 3/2)
slope = (13/3) / (-9/2)
slope = (13/3) * (-2/9)
slope = -26/27
So, the correct answer is C. 26/27.
1. To express the relationship between distance and time as a unit rate, you need to determine how many miles are driven per hour. You can do this by finding the ratio between the distance and time. For example, for the first pair (4 hours and 204 miles):
Distance/time = 204 miles / 4 hours = 51 miles/hour
So, the relationship between distance and time in simplified form as a unit rate is 51/1. Therefore, the correct statement is: A. 51/1; your car travels 51 miles every 1 hour.
2. To find the slope of a line passing through two points, you can use the formula:
slope = (y2 - y1) / (x2 - x1)
Using the provided points (2, 5) and (8, 3):
slope = (3 - 5) / (8 - 2) = -2 / 6 = -1/3
So, the slope of the line passing through the points (2, 5) and (8, 3) is -1/3. Therefore, the correct answer is: B. -1/3.
3. To find the slope of the line passing through the points (3/2, -2) and (-3, 7/3), you use the same formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the values:
slope = (7/3 - (-2)) / (-3 - 3/2) = (7/3 + 6/3) / (-9/2 - 3/2) = 13/3 / (-12/2) = 13/3 / (-6) = -13/18
So, the slope of the line passing through the points (3/2, -2) and (-3, 7/3) is -13/18. Therefore, the correct answer is: C. 26/27.