Full Answer Section

Substituting the values:

m = (8 – 3) / (10 – 2) m = 5 / 8

Therefore, the slope of the flight path is 5/8.

Writing the Equation in Slope-Intercept Form:

Now, using the slope (m) and any one of the coordinate points (x1, y1) or (x2, y2), we can write the equation of the line in slope-intercept form:

y = mx + b

Here, let’s use the departure point (2, 3):

y = (5/8) x + b

Finding the y-Intercept (b):

To find the y-intercept (b), we can substitute the values of x and y from the departure point back into the equation:

3 = (5/8) * 2 + b

Solving for b:

3 = 5/4 + b b = 3 – 5/4 b = 7/4

Therefore, the equation of the plane’s flight path in slope-intercept form is:

y = (5/8) x + 7/4

Significance of the Components:

• Slope (m): The slope of 5/8 indicates that for every 5 units the plane flies horizontally (increase in x), it climbs 8 units vertically (increase in y). This translates to a relatively steep ascent angle.
• y-Intercept (b): The y-intercept of 7/4 represents the initial height of the plane at the departure point (2, 3). In this case, it indicates that the plane starts at an altitude of 7/4 units above the ground at the starting point.

Summary:

The equation y = (5/8) x + 7/4 describes the flight path of the plane, considering the departure and arrival coordinates. The slope indicates the ascent angle, and the y-intercept reveals the initial altitude. This information can be useful for various purposes, such as tracking the plane’s movement, calculating ground clearance at different points, or even predicting arrival time based on its trajectory.