time H: 5 10 15 20
dist mi 6 12 18 24
slope:
Unit rate:
The unit rate of time with respect to distance is 3. This means that for every 6 miles traveled, 5 hours have passed.
To find the slope of the given data, we need to calculate the unit rate. The unit rate represents the rate of change in the dependent variable (distance) for a 1-unit change in the independent variable (time).
In this case, the independent variable is time (H) and the dependent variable is distance (dist mi).
To calculate the unit rate, we can use the formula:
Unit Rate = Change in dependent variable / Change in independent variable
Let's calculate the unit rate using the given data points:
For the first pair of data points:
Change in distance = 12 - 6 = 6
Change in time = 10 - 5 = 5
Unit Rate = 6 / 5 = 1.2
For the second pair of data points:
Change in distance = 18 - 12 = 6
Change in time = 15 - 10 = 5
Unit Rate = 6 / 5 = 1.2
For the third pair of data points:
Change in distance = 24 - 18 = 6
Change in time = 20 - 15 = 5
Unit Rate = 6 / 5 = 1.2
Therefore, the unit rate (slope) for the given data is 1.2.
To find the unit rate or slope, we can calculate the change in distance divided by the change in time.
Change in distance = 24 - 6 = 18 mi
Change in time = 20 - 5 = 15 H
Unit rate (slope) = Change in distance / Change in time
= 18 mi / 15 H
Simplifying the unit rate (slope) gives us:
Unit rate (slope) = 6/5 mi/H
but what is the slope
The slope represents the rate of change between two variables. In this case, the slope represents the rate of change between time and distance.
To calculate the slope, we can use the formula:
slope = change in distance / change in time
Using the given data points:
For the first pair of data points:
Change in distance = 12 - 6 = 6 mi
Change in time = 10 - 5 = 5 H
slope = 6 mi / 5 H = 1.2 mi/H
For the second pair of data points:
Change in distance = 18 - 12 = 6 mi
Change in time = 15 - 10 = 5 H
slope = 6 mi / 5 H = 1.2 mi/H
For the third pair of data points:
Change in distance = 24 - 18 = 6 mi
Change in time = 20 - 15 = 5 H
slope = 6 mi / 5 H = 1.2 mi/H
Therefore, the slope for the given data is 1.2 mi/H.