The Kwon family has a rainwater catchment system they use to water their garden. After 3 days without rain, the depth of water in the tanks is 63 inches. After 5 days, the depth is 57 inches. Write an equation in point-slope form describing the situation

y-63 = (57-63)/(5-3) (x-3)

To write an equation in point-slope form, we need to determine the slope and a point on the line. In this case, the slope represents the rate at which the depth of water decreases each day, and the point on the line represents the initial depth of water.

Let's first find the slope. The change in depth is given by:
Change in depth = final depth - initial depth
Change in depth = 57 inches - 63 inches
Change in depth = -6 inches

Since this change occurs over a period of 5 days, the slope of the line is the change in depth divided by the number of days, which is:
Slope = -6 inches / 5 days

Now, let's find a point on the line. We know that after 3 days without rain, the depth of water is 63 inches. So our point is (3, 63), where 3 represents the number of days and 63 represents the depth of water.

Now we can write the equation in point-slope form using the slope and the point:
y - y1 = m(x - x1)

Substituting the values we have:
y - 63 = (-6/5)(x - 3)

Simplifying the equation gives us the equation in point-slope form:
y - 63 = (-6/5)x + (6/5) * 3

Further simplifying:
y - 63 = (-6/5)x + 18/5

This is the equation in point-slope form that describes the situation.