standard from Ax +By = C
y = 4x+10
subtract 4x from each side
-4x+y = 10
or 4x - y = -10
A) One solution: 5x +2y = 0 . . . . (any line with a different slope)
b) Two solutions: not possible
c) No solutions: 5x -2y = 0 . . . . (any different line with the same slope)
d) Infinitely many solutions: 10x -4y = 6 . . . . (any other equation for the same line)
a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is

b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so

c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so

Then by linearity, we have
