Answer:
Plane A:
The rate of change or slope of function A is: m = 470
It means plane A is flying 470 miles per hour.
Thus, the rate of speed of plane A is 470 miles per hour.
Plane B:
The rate of change or slope of Plane B is: m = 480
It means Plane B is flying 480 miles per hour.
Thus, the rate of speed of plane A is 480 miles per hour.
Therefore, we conclude:
- Plane B is flying faster.
Step-by-step explanation:
The slope-intercept form of the line equation
![y = mx+b](https://tex.z-dn.net/?f=y%20%3D%20mx%2Bb)
where
- m is the rate of change or slope
Plane A
From the given equation
y = 470x
where
x is the time that plane flies in hours
y is the distance the plane flies in miles
Thus, comparing with the slope-intercept form y = mx+b
The rate of change or slope = 470
It means plane A is flying 470 miles per hour.
Plane B
Given the table
Time (h) 1 2 3 4
Distance (mi) 480 960 1440 1920
Finding the slope by taking any two points, let say, (1, 480) and (2, 960)
![\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cmathrm%7BSlope%7D%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![\left(x_1,\:y_1\right)=\left(1,\:480\right),\:\left(x_2,\:y_2\right)=\left(2,\:960\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2C%5C%3Ay_1%5Cright%29%3D%5Cleft%281%2C%5C%3A480%5Cright%29%2C%5C%3A%5Cleft%28x_2%2C%5C%3Ay_2%5Cright%29%3D%5Cleft%282%2C%5C%3A960%5Cright%29)
![m=\frac{960-480}{2-1}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B960-480%7D%7B2-1%7D)
Refine
![m=480](https://tex.z-dn.net/?f=m%3D480)
Therefore, the rate of change or slope of Plane B is: m = 480
It means Plane B is flying 480 miles per hour.
Conclusion:
Plane A:
The rate of change or slope of function A is: m = 470
It means plane A is flying 470 miles per hour.
Thus, the rate of speed of plane A is 470 miles per hour.
Plane B:
The rate of change or slope of Plane B is: m = 480
It means Plane B is flying 480 miles per hour.
Thus, the rate of speed of plane A is 480 miles per hour.
Therefore, we conclude:
- Plane B is flying faster.