Çözüldü Linear Functions - Analytic Geometry

Adapted from a "SAT Subject Test Math Level 2" question:

If a linear function, f, has a slope of -2, and passes through the points (1, 2) and (2, q), what is the area of the region between the function and the coordinate axes?

-2 = (2 - q) / (1 - 2) ⇒ 2 = 2 - q ⇒ q = 0
Equation of the linear function (line) y = f(x); (y - 2) / (2 - 0) = (x - 1) / (1 - 2) ⇒ y = f(x) = -2x + 4
x intercept is 0 = -2x + 4 ⇒ x = 2
y intercept is y = f(0) = -2(0) + 4 = 4
Area of the region (triangle): 2·4 / 2 = 4 square units.