Answer:
9. 9x -4y = -36
10. geometric; terms have a common ratio of 1/2. Never 0 or negative; 1/2 times a positive number is a positive number.
Explanation:
You want the equation of the line with x-intercept (-4, 0) and y-intercept (0, 9), and you want to know if the sequence 40, 20, 10, 5, ... is arithmetic.
9. Line
It is helpful to know a few different forms of the equation for a line. One of them is "intercept form," x/a +y/b = 1, where 'a' and 'b' are the x- and y-intercepts, respectively.
For intercepts (-4, 0) and (0, 9), the equation in this form is ...
x/(-4) +y/9 = 1
Multiplying by -36 puts it in standard form:
9x -4y = -36
10. Sequence
(a) First differences of the sequence 40, 20, 10, 5 are ...
-20, -10, -5 . . . . . not constant
Since the first differences are not constant this is not an arithmetic sequence.
Ratios of successive terms are ...
20/40 = 10/20 = 5/10 = 1/2 . . . . . . constant
A sequence of terms with a common ratio is a geometric sequence. This sequence has a common ratio, so is geometric.
(b) The common ratio is 1/2, a positive number. The given terms of the sequence are positive numbers. Each successive term is 1/2 the previous term, so all terms will be positive—never 0 or negative. (The product of two positive numbers is always positive.)