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 tank is 63 inches. After 5 days, the depth is 57 inches. Write an equation in point-slope form describing the situation.
To write an equation in point-slope form, we need the slope and a point. The points given to us by the explanation are (3, 63) and (5, 57) where the x value represents the number of days without rain and the y value represents the depth of the water in inches.
To find the slope, we use the expression: Change in y/change in x = 63-57/3-5 When simplified, we get: 6/-2 = -3
Therefore, the slope is -3
Note that we can use either of the points in our equation and we will still get the same equation.
Now we just need to substitute in our values:
y = -3(x-3) + 63 which is sometimes written as y - 63 = -3(x-3)
