Robi has run the first 4 miles of a race in 30 minutes. She reached the 6 mile point after 45 minutes. What is the slope?
Usually, time would be on the x-axis.
slope is change in y/change in x
slope = (6-4)/(45-30)
slope = 2/15 miles/minute
Thank you so much
To find the slope, we first need to determine the change in distance and change in time.
Change in distance = final distance - initial distance
Change in distance = 6 miles - 4 miles = 2 miles
Change in time = final time - initial time
Change in time = 45 minutes - 30 minutes = 15 minutes
Now, we can calculate the slope by dividing the change in distance by the change in time:
Slope = Change in distance / Change in time
Slope = 2 miles / 15 minutes
To simplify the slope, we can convert the speed from minutes per mile to miles per hour by multiplying by 60:
Slope = (2 miles / 15 minutes) * (60 minutes / 1 hour)
Slope = 8 miles / hour
Therefore, the slope is 8 miles per hour.
To find the slope, we need to determine the rate at which Robi is running.
The slope, also known as the rate of change or the speed, is calculated by finding the difference in the vertical (y-axis) values divided by the difference in the horizontal (x-axis) values. In this case, the vertical values represent the distance covered (in miles), and the horizontal values represent the time spent running (in minutes).
Let's start by labeling the values we are given:
Point 1: (x1, y1) = (30 minutes, 4 miles)
Point 2: (x2, y2) = (45 minutes, 6 miles)
We can now calculate the slope using the formula:
Slope = (y2 - y1) / (x2 - x1)
Substituting the values into the formula, we have:
Slope = (6 miles - 4 miles) / (45 minutes - 30 minutes)
Slope = 2 miles / 15 minutes
To simplify the fraction, we can convert minutes to hours. There are 60 minutes in an hour, so 15 minutes is equal to 15/60 = 1/4 hour.
Slope = 2 miles / (1/4) hour
To divide by a fraction, we can multiply by the reciprocal of the fraction:
Slope = 2 miles * (4/1) hour
Slope = 8 miles / 1 hour
Therefore, the slope of Robi's performance is 8 miles per hour.