Question

Select the correct answer.

Time
(weeks) Lake Depth
(feet)
0 346.0
2 344.8
5 343.0
7 341.8
10 340.0
12 338.8

An environmental agency studying the effects of drought on a lake found that the water level decreased at a constant rate during the first few months of the drought. When the agency began its research, the depth of the lake was 346 feet. The table represents the agency’s susequent observations about the lake's depth.

Which equation represents the depth of the lake, y, based on the number of weeks passed, x?

A. y = -0.6x + 346
B. y = -1.2x + 346
C. y = -0.6x
D. y = -1.2x

Answer 1

A. y = -0.6x + 346

Explanation:

Let time be x and the depth be y,

we use the linear equation,

y = mx + b,

Then, initially, for 0 weeks or when x = 0,

the depth was 346

so, y = 346,

and the general equation becomes for x = 0,

y = m(0) + b

y = b

Comparing with the result we got, we have,

b = 346

Now, when x = 5, y = 343,

putting into the general equation,

343 = m(5) + 346

343 - 346 = 5m

-3 = 5m

m = -3/5

m = -0.6

Hence we get the equation,

y = -0.6x + 346