An airplane has begun its descent for a landing. When the airplane is 150 miles west of its destination, its altitude is 32,000 feet. When the airplane is 100 miles west of its destination, its altitude is 14,000 feet. If the airplane's descent is modeled by a linear function, where will the airplane be in relation to the runway when it hits ground level? A) airplane will over shoot the runway by 61 feet B) airplane will over shoot the runway by 610 feet C) airplane will land short of the runway by 61 feet D) airplane will land short of the runway by 6.1 feet

It is given that, when the airplane is 150 miles west of its destination, its altitude is 32,000 feet. When the airplane is 100 miles west of its destination, its altitude is 14,000 feet.

The airplane's descent is modeled by a linear function.

If linear function passing through two points, then the equation of line is

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

x-coordinate represents the distance in miles west of its destination and y-coordinate represents the altitude at that point.

The plane passing through (-150,32000) and (-100,14000).

The equation of line is

[tex]y-32000=\frac{14000-32000}{-100+150}(x+150)[/tex]

[tex]y-32000=-360(x+150)[/tex]

[tex]y-32000=-360x-54000[/tex]

[tex]y=-360x-54000+32000[/tex]

[tex]y=-360x-22000[/tex]

The value of y is 0, when airplane be in relation to the runway when it hits ground level.

[tex]0=-360x-22000[/tex]

[tex]22000=-360x[/tex]

Divide both sides by -360.

[tex]\frac{22000}{-360}=x[/tex]

[tex]-61.11=x[/tex]

The value of x is negative, therefore the correct option is A.