I have a problem with variables and expressions. the paper says name the rule. y=1, 5 and 7 the answers are 9,5 and 3. how do i figure out what the...

Given the values of y are : 1, 5, and
7

Also, given the values of x are : 9, 5, and
3.

Then, we will rewrite as
pairs.

==> ( 9, 1) (5,5) and ( 3,
7)

We will find the slope for each two
points.

==> (9,1) and
(5,5)

==> m1 = (5-1)/(5-9)= (4/-4 =
-1

==> m1=
-1

==> (9,1) and
(3,7)

==> m2=
(7-1)/(3-9)

==> m2= 6/-6 =
-1

==> (3,7) and
(5,5)

==> m3= (7-5)/(3-5) = 2/-2 =
-1

==> m3= -1

We notice
that m1= m2 = m3 = -1

Then, the three points are on the
same graph or have the same equation.

Then we will find the
equation using one of the points and the slope m= -1

We
will use the point (5, 5)

==> y-y1 =m
(x-x1)

==> y- 5 = -1 (
x-5)

==> y= -x + 5 +
5

==> y= -x +
10

Then, the rule that satisfies all three
points is : y= -x + 10