Question

Rearrange the equation so xis the independent variable.

Answer 1

INTERESTING

Explanation:

Answer 2

`y=5(x-4)-6\\` or
`y=5x-26`

Explanation:

How we want the right side of the equation to look is entirely up to us, but the key to this problem is in getting y by itself. We basically want to turn this equation into a machine where we can punch in any value of x we want (it's independent because we have the freedom to choose (is free choice a thing? I'll leave that question to the philosophers)) and get out some value of y (the dependent variable, because it pops out from - or depends on - our choice of x).

So, we'll need to unwrap y from any operations connecting it to other numbers. In the equation
`y+6=5(x-4)`, y is connect to 6 by addition, so we can unwrap that addition with subtraction, making sure we subtract 6 from both sides to keep the equation balanced. This gives us

`y=5(x-4)-6`, which is perfect fine (and an incredibly useful form when you get to the topic of function transformations), but if we pick a value for x, we need to perform three different operations:

• Subtraction by 4
• Multiplication by 5
• Subtraction by 6

We can do better. If we simplify the right side, we can make our machine more efficient:

`y=5(x-4)-6=5x-20-6=5x-26\\y=5x-26`

Now if we pick a value for x, we'll only need to

• Multiply by 5
• Subtract 26

So if we pick x = 6, for instance:
`y=5(6)-26=30-26=4`, and that's just a little bit nicer.