Question

An airplane has begun its descent for a landing. When the airplane is 150 miles west of its destination, its altitude is 25,000 feet. When the airplane is 90 miles west of its destination, its altitude is 19,000 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?

Answer 1

we have two points on a plane p1(150, 25000), p2(90, 19000) and we can find a linear equation from them, lets calculate the slope:
m = (y2 - y1)/(x2 - x1)
where x1, y1 and x2, y2 are the point's coordinates:
m = (19000 - 25000)/(90 - 150)
m = -6000/-60
m = 100
so we have the slope now, and we can use the equation of the line for a point and having the slope, that equation is:
y - y1 = m(x - x1)
so we substitute:
y - 25000 = 100(x - 150)
y = 100x + 25000 - 15000
y = 100x + 10000
so this is the linear equation that models the airplane descent, when the airplane hits the ground, then y = 0, and we need to find the x, that is the position in relation to the runway:
0 = 100x + 10000
-100x = 10000
x = -100