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# the depth of a farm pond is changing according to the equation y=12-2x, where x= depth in meters and x= time in weeks

The problem states that the depth of a farm pond is changing according to the equation   y = 12 - 2x   , where y is the depth of the pond (in meters) and x is the time (in weeks).

If you rearrange the equation given, you will find that it is in slope-intercept form. That is,

y = 12 - 2x     ==>     y = -2x + 12

Recall that the slope-intercept form of a linear equation is the following:     y = mx + b ,

where m is the slope of the line and b is the y-intercept.

The slope, m, of a line is its average rate of change and the y-intercept, b, is the point at which the line crosses the y-axis (i.e., the point at which x = 0).

I'm assuming the problem is asking you to find the average rate of change of the depth of the pond, which is the slope, m, of the equation representing this change in depth.

y = -2x + 12     ==>     m = -2     and     b = 12

From this, we can conclude that the average rate of change of the depth of the pond is -2. That is, the depth of the pond is decreasing at a rate of 2 meters per week.

Also, since the y-intercept is 12, we find that the depth of the pond is 12 meters at time (in weeks) equals 0 (i.e., at x = 0).

So, if the depth of the pond is 12 meters at the beginning (i.e., week 0) and the rate of the change of the pond is decreasing by 2 meters per week, then we can when the depth of the pond will equal 0 meters:

week 0   ==>   12 meters

week 1   ==>   12 - 2 = 10 meters

week 2   ==>   10 - 2 = 8 meters

week 3   ==>    8 - 2 = 6 meters

week 4   ==>    6 - 2 = 4 meters

week 5   ==>    4 - 2 = 2 meters

week 6   ==>    2 - 2 = 0 meters

I'm assuming you meant:

y = depth in meters

x = time in weeks

using the equation

y = 12 - 2x you can see that at x = 0 the height of the pond is 12 m

y = 12 - 2*(0) = 12

and then when x = 6 the height of the pond will be zero

0 = 12 - 2x

2x = 12

x = 6

the rate of change (slope) is -2 and that means that the height is decreasing by 2 meters per week

I'm not sure what you were tasked with trying to solve for but that's all that I can think of mentioning based on the information you gave.

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