Question

I really only need help on Part A, but if someone could clarify all of them, that would be awesome! Please help, I'm up really late trying to finish this and I could really use some sleep.

Thanks in advance!

~Micah K.

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x + 2 intersect are the solutions of the equation 4x = 2x + 2.

Part B: Make tables to find the solution to 4x = 2x + 2. Take the integer values of x between -3 and 3.

Part C: How can you solve the equation 4x = 2x + 2 graphically?

Answer 1

so you are plotting 4x and 2x+2. so they will be two separate lines. they will cut each other at only one point. that is the only common point of the graphs y=4x and y=2x+2. so that point is the only solution of 4x=2x+2

Answer 2

any confusion regarding part A @micahpkay ??

Answer 3

But how do I explain how the x coordinate where the lines intersect is the solution to the system of equations? I know that it is, but I don't know how or why. These questions are worded very poorly, in my opinion. @Arnab09

Answer 4

in other words, first graph is the solution for y-4x=0.....i
second graph is the solution for y-(2x+2)=0........ii
only at the point of intersection these two equations satisfy both, because that is the only common point.
so, you can subtract (ii) from (i), you are left with -4x+2x+2=0, or 4x=2x+2

Answer 5

you see, that y part is canceled out if you subtract, but you can only subtract when those equations both are satisfied at a point, that is the point of intersection

Answer 6

I get what you're saying, but it's kind of confusing.

Answer 7

what's confusing you? @micahpkay

Answer 8

Your wording, I guess. Wording always confuses me.

Answer 9

okay, give it some time then

Answer 10

Give what some time?

Answer 11

try to understand what i said, and make some research in internet for your clarification

Answer 12

I really hate problems like this.....

Answer 13

When you said "only at the point of intersection these two equations satisfy both," what is 'both?"

Answer 14

both equations are satisfied at that point only, no other point on the graph

Answer 15

Also, I don't get this part:

"so, you can subtract (ii) from (i), you are left with -4x+2x+2=0, or 4x=2x+2"

Answer 16

there are two equations numbered i and ii, see above.. Left hand sides and right hand sides are subtracted, so we are left with -4x=2x+2, in the next step you can take 4x in right hand side, 2x+2=4x

Answer 17

Can you write that part out step by step?

Answer 18

y-4x=0
y-(2x+2)=0
we are subtracting left hand side as well as right hand side to take it down to one equation, as both equations are satisfied at the point of intersection.
so, y-4x-{y-(2x+2)}=0-0
y-4x-y+2x+2=0
y terms are cancelled out as you can clearly see,
so -4x+2x+2=0
4x=2x+2

Answer 19

Okay, thanks a lot!

Answer 20

So is it like this?

-4^x + 2^x + 2 = 0

-4^x + 2^x + 2 - 2^x + 2 = 0 - 2^x + 2

-4^x = -2^x + 2

4^x = 2^x + 2

Answer 21

exactly, though get rid of those power signs

Answer 22

Why?

Answer 23

because the given equation does not involve power relation

Answer 24

Yes it does.

Answer 25

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4x and y = 2x + 2 intersect are the solutions of the equation 4x = 2x + 2.
can you explain where it has exponential relation?

Answer 26

It didn't copy and paste correctly. Does that affect your answers?

Answer 27

oh, that does not affect, basic concept is same..

Answer 28

Okay.

Answer 29

Can i ask one more question, @Arnab09 ?

Answer 30

yeah, sure

Answer 31

Okay, I'll close this question and post another one so that you can get another medal and so other people who are searching for an answer can find it more easily.

Answer 32

sure