The value of r is varying at a constant rate of change with respect to s.

Question

The value of r is varying at a constant rate of change with respect to s.

1. Complete the following table.

s (value of the independent quantity)	r (value of the dependent quantity)
1	15
3	9
9	-9
12	-18

1. Define a formula that represent Δr in terms of Δs. Hint
2.     
3. What is the value of r when s=0?
4. r=
5. Define a formula to represent r in terms of s.

Answer 1

Hello, Samatha,

It often helps to graph points such as these so that we can visualize what is happening. The problem states that there is a constant rate of change, which infers a straight line. The slope of that line is the rate of change. By looking at the data we can see that it must be negative - as s increases, r decreases. Just looking at the first 2 points, we see that the rate of change, (delta r/delta s), is (-6/2) or -3. We see the same change for the other points (e.g., (-9-9)/(9-3) =-18/6, or -3).

A graph will show this to be a straight line with a slope of -3. We need to find the intercept, b, of the straight line.

The traditional y = mx+b may be used, but for this problem we use r in place of y, and s instead of x.

Use a slope of -3 to get r = -3s + b

We know the first point, (1,15) lies on this line (is a solution), so use that point (or any of the others) to find the intercept, b.

15 = -3*1 + b

b = 18

now we have r = -3s + 18

Try some of the other points to confirm that this relationship is correct.

(9,-9): Let's see if our equation predicts r to be -9 if we use 9 for s: r = -3*9 + 18 r=-9 Yes

You can check the other points to be certain we have the right equation.

Now we can find r when s = 0: r = -3*0 + 18; therefore r = 18

I hope this helps,

Bob