Use a absolute value to write a rule for determining the distance between two points on a coordinate plane that have the same x-coordinate

For two points (x,a) and (x,b), the distance would be |a-b| or |b-a| both would be the same.

Step-by-step explanation:

What is the rule without an absolute value?  basically we are looking for the difference (which is the answer to a subtraction problem) between the two.

Say the two points are (x,a) and (x,b)  So they have the same x value but different y values.  Now, when you want to take the difference you usually want to subtract the smaller number from the larger, but hat happens if you don't?  So instead subtract the larger number from the smaller number?  I'm gonna show a few examples.

7-5 = 2

5 - 7 = -2

7 - 3 = 4

3 - 7 = -4

As you can see, no matter which order you subtract you will always get the same number, just either positive of negative.  We are going to use that.  Basically, we can have the two in either order, as long as we have them inside of an absolute value, we will always get the same answer.

so, for our two y values, a and b, it doesn't matter which is larger |a-b| = |b-a| and this is the distance.  

its kind of blurry. can you put a clearer pic?

step-by-step explanation:

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.