Answer:
[tex]y=5(x-4)-6\\[/tex] or [tex]y=5x-26[/tex]
Step-by-step 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 [tex]y+6=5(x-4)[/tex], 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
[tex]y=5(x-4)-6[/tex], 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:
[tex]y=5(x-4)-6=5x-20-6=5x-26\\y=5x-26[/tex]
Now if we pick a value for x, we'll only need to
So if we pick x = 6, for instance: [tex]y=5(6)-26=30-26=4[/tex], and that's just a little bit nicer.
