Calculation of a plane at the coordinates

Sample Solution

Determining the Plane's Flight Path Equation

1. Slope Calculation:

The slope (m) of a line represents the rise over run between two points. In this case, the rise is the change in y-coordinate (8 - 3 = 5) and the run is the change in x-coordinate (10 - 2 = 8). Therefore, the slope (m) is:

m = rise / run = 5 / 8

2. Equation in Slope-Intercept Form:

We have the slope (m = 5/8) and one point (2, 3). We can use the point-slope form of the equation (y - y1 = m(x - x1)) to solve for the y-intercept (b):

y - 3 = (5/8)(x - 2)

Distributing and rearranging the equation, we get the slope-intercept form:

Full Answer Section

y = (5/8)x - 11/8

3. Significance of Components:

• Slope (m = 5/8): This value tells us that for every 5 units the plane moves horizontally (along the x-axis), it gains 8 units of altitude (along the y-axis). It represents the plane's overall direction and rate of climb.
• Y-intercept (b = -11/8): This value represents the initial altitude of the plane at the point (2, 3). Since it's negative, it indicates that the plane starts below the y-axis (possibly on a runway or taxiway).

4. Additional Notes:

• This equation assumes a straight-line flight path. In reality, the plane's path might involve curves or changes in slope during takeoff and climb.
• The equation only considers the two given points and doesn't account for potential changes in direction or altitude later in the flight.

I hope this explanation clarifies the calculations and the significance of each component in the equation related to the plane's flight path.