Can anyone help me with this in-out table?

Question

in - out

-4 = 7

-2 = 1

0 = -5

2 = -11

4 = -17

6 = -23

if you could explain how you did it that would be great, thanks!

Answer 1

Start by guessing that the rule is some linear equation.  Call the number that goes in x and the number that comes out y.  Then you know that y = ax + b where a and b are some constants.  You need to solve for a and b to find the rule.  The table gives you solutions (x,y) to the equation.  So, since (0, -5) is a solution because when 0 is plugged in as x then -5 is taken out as y, plug this into your equation to solve for b.

y = ax + b

-5 = a*0 + b

-5 = b

Since b = -5, you know that the rule is given by y = ax - 5.  All you need now is the value of a.  So, use any other pair in the table to solve for a.  I'll use (-2, 1)

y = ax - 5

1 = a(-2) - 5

1 = -2a - 5   ...add 5 to both sides

1 + 5 = -2a

6 = -2a   ...divide both sides by -2

6/-2 = a

-3 = a

Since a = -3 and b = -5, the equation is y = -3x - 5.  Check and make sure that this rule gives the correct output for all of the inputs in the table.  

When x = -4 then y = -3*(-4) - 5 = 12 - 5 = 7.  Good.

When x = -2 then y = -3*(-2) - 5 = 6 - 5 = 1.  Good.

When x = 0 then y = -3*(0) - 5 = -5.  Good.

When x = 2 then y = -3*(2) - 5 = -6 - 5 = -11.  Good.

When x = 4 then y = -3*(4) - 5 = -12 - 5 = -17.  Good.

When x = 6 then y = -3*(6) - 5 = -18 - 5 = -23.  Good.

Hope this helps you!