If (x, y) ---> (x + 6, y - 4), find the pre-image of (9, -2). *

The coordinates of the pre-image of (9, -2) will be: (3, 2)

Step-by-step explanation:

Given the translation rule:

(x, y) → (x + 6, y - 4)

This translation indicates that the image of the original object must have been determined by adding 6 units (moving right) to the x-coordinate and subtracting 4 units (moving down) to the y-coordinate.

Given the image

According to the translation rule (x, y) → (x + 6, y - 4)

(x, y) → (x + 6, y - 4)

Determining the x-coordinate of the pre-image:

x+6 = 9

x = 9-6

x = 3

Determining the y-coordinate of the pre-image:

y-4 = -2

y = -2+4

y = 2

Thus, the coordinates of the pre-image of (9, -2) will be: (3, 2)

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.