To find the slope of the line representing the flight path, we can use the slope formula:

slope (m) = (y2 - y1) / (x2 - x1)

Using the given coordinates, (2,3) and (10,8), we can substitute the values into the formula:

m = (8 - 3) / (10 - 2)
m = 5 / 8

So, the slope of the flight path line is 5/8.

To write the equation of the line in slope-intercept form (y = mx + b), we need to find the y-intercept (b).

Using the point-slope form of a line (y - y1) = m(x - x1), where (x1, y1) are the coordinates of a point on the line and m is the slope, we can choose one of the given points, let's say (2,3), and substitute the values:

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

Simplifying this equation, we get:

y - 3 = (5/8)x - 5/4

To isolate y, we can add 3 to both sides:

y = (5/8)x + (5/4) + 3
y = (5/8)x + (5/4) + 12/4
y = (5/8)x + 17/4

So, the equation of the flight path line is y = (5/8)x + 17/4.

In this equation, the component (5/8) represents the slope of the line, which indicates how steep the plane's flight path is. A positive slope indicates an upward trajectory, and a larger absolute value of the slope represents a steeper ascent.

The component (17/4) represents the y-intercept, which is the point where the flight path intersects the y-axis. In this case, the value 17/4 indicates that the plane was above the ground (y-axis) even from the beginning of its flight.

Overall, the equation y = (5/8)x + 17/4 gives us a mathematical representation of the plane's flight path, indicating the slope and the initial height.

Got a question with my answer?

Message Me

Cheapmath.com is completely free!

Asking question is free. Getting answers is free.

+99

Continue