# 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 expression is?

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### 1 Answer

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**