Question

Find the area of a parallelogram bounded by the y-axis, the line x=3, the line f(x)=1+2x,and the line parallel to f(x) passing through (2, 7).

Answer 1

6 square units

Explanation:

The parallel line has equation ...

y -7 = 2(x -2)

y = 2x + 3

The y-intercept of this one differs from the given line by 3-1 = 2, so that is the length of the "base" of the parallelogram. The "height" is the distance between the parallel lines x=0 and x=3, which is 3-0 = 3. Then the area is ...

A = bh = 2·3 = 6 . . . . square units