The linear equation −2x+3y=−6 can be rearranged to the form y=mx+b, where m is the slope and b is the y-intercept.
Rearranging the equation, we get:
3y = 2x - 6
y = (2/3)x - 2
The corresponding graph should have a slope of (2/3) and a y-intercept of -2.
Option C matches this criteria.
Which graph matches the linear equation: −2x+3y=−6
3 answers
The tables below show the number of jumping jacks completed after a given period of time in seconds. Kimberly: Time (seconds) Jumping Jacks 3 17 8 37 12 53 16 69 Katrina: Time (seconds) Jumping Jacks 2 10 5 25 12 60 20 100(3 points) a. Which person is doing more jumping jacks per second? b. Which person had done more jumping jacks initially before the timer started? c. Which person shows a proportional relationship?
a. The person doing more jumping jacks per second can be determined by finding the average rate of change of jumping jacks over time.
For Kimberly:
The average rate of change between 3 seconds and 16 seconds is (69-17)/(16-3) = 4 jumping jacks per second.
For Katrina:
The average rate of change between 2 seconds and 20 seconds is (100-10)/(20-2) = 5 jumping jacks per second.
Therefore, Katrina is doing more jumping jacks per second.
b. To determine which person had done more jumping jacks initially before the timer started, we can look at the first point in each table.
For Kimberly:
Kimberly had done 17 jumping jacks at 3 seconds.
For Katrina:
Katrina had done 10 jumping jacks at 2 seconds.
Therefore, Kimberly had done more jumping jacks initially before the timer started.
c. A proportional relationship exists when the ratio of the number of jumping jacks to the time elapsed remains constant.
For Kimberly:
The ratio of jumping jacks to time elapsed ranges from 17/3 to 69/16. The ratios are not constant, so there is no proportional relationship.
For Katrina:
The ratio of jumping jacks to time elapsed ranges from 10/2 to 100/20. The ratios are constant (5/1), so there is a proportional relationship.
Therefore, only Katrina shows a proportional relationship.
For Kimberly:
The average rate of change between 3 seconds and 16 seconds is (69-17)/(16-3) = 4 jumping jacks per second.
For Katrina:
The average rate of change between 2 seconds and 20 seconds is (100-10)/(20-2) = 5 jumping jacks per second.
Therefore, Katrina is doing more jumping jacks per second.
b. To determine which person had done more jumping jacks initially before the timer started, we can look at the first point in each table.
For Kimberly:
Kimberly had done 17 jumping jacks at 3 seconds.
For Katrina:
Katrina had done 10 jumping jacks at 2 seconds.
Therefore, Kimberly had done more jumping jacks initially before the timer started.
c. A proportional relationship exists when the ratio of the number of jumping jacks to the time elapsed remains constant.
For Kimberly:
The ratio of jumping jacks to time elapsed ranges from 17/3 to 69/16. The ratios are not constant, so there is no proportional relationship.
For Katrina:
The ratio of jumping jacks to time elapsed ranges from 10/2 to 100/20. The ratios are constant (5/1), so there is a proportional relationship.
Therefore, only Katrina shows a proportional relationship.
1 answer