Question

Write the standard form of an equation for the graph described.
Line passing through (1,1) and (1,10)

Answer 1

if your x coordinate is the same, and the line goes straight up from y=1 to y=10, what can you tell about this line?

This line is ________\(.\)

Answer 2

Vertical?

Answer 3

...Vertical?

Answer 4

I mean if it goes straight up...

Answer 5

Yes. That's right. Do you have any ideas on how you might describe a vertical line?

Answer 6

What do you mean?

Answer 7

Yes, you got it, the line is vertical.

Answer 8

((The question doesn't ask to describe the vertical line, does it...? In any case, I have to leave for a minute))

Answer 9

I imagine they're being asked to put it in the form y=mx+b, is that right tw? You've been plotting with slope and y intercept, but this one is weird because it doesn't really have a slope.

Answer 10

no, I just need to figure out the standard form of an equation for a line that passes through those points.

Answer 11

Yes, thats whats got me hung up.

Answer 12

Alright. Let's think back to what an equation really it. It's relating x to y right? When you first started learning how to do these, you might have made a chart like

x | y
____
1 | 2
2 | 4
3 | 6
4 | 8

Answer 13

And that would describe y =2x right?

Answer 14

Yes. I thought I needed to try and find the slope through y1-y2/X1-x2 but I didn't know if that was right.

Answer 15

Normally that would work, but I imagine you tried that and got that

10-1 / 1-1
=
9/0 which doesn't make sense, because you can't divide by 0.

Answer 16

So we have to be clever with this problem and think of something new.

Answer 17

If it helps, the answers are
-x=-1
X=3
X+y=11
X+0y=11
X+0y=1

Answer 18

Ooh okay.

Answer 19

So, if we were to make for this graph it might look like this right?

Answer 20

Does that graph make sense?

Answer 21

Yes

Answer 22

Im really sorry if my responses are lagging, this website always makes my computer slow.

Answer 23

So let's go back to making charts, and like you had to do when you were first learning this, see if we can notice any pattern, anything that's true.

x | y
----
1| -1
1| 0
1| 1
1| 2
1| 3
1| 4
...

Answer 24

So what I've done there is I've taken a whole bunch of points on the graph right?

Can you tell me anything you notice about it? Any patterns?

Answer 25

umm well i see that x stays the same but y can move around

Answer 26

That's good. How would you describe that in mathematical terms? "X stays the same" ?

Answer 27

x is consistent?

Answer 28

That's good, you get the concept. Can you say "X is consistently and always 1" in an equation?

Answer 29

yes

Answer 30

How would you say "X is 1" with an equation?

Answer 31

by substituting?

Answer 32

Can you expand on that?

Answer 33

Try not to overthink it by the way.

Answer 34

like y=mx+b it would be y=m(1)+b?

Answer 35

Well, mx + b doesn't see to work because we don't have a slope right?

Answer 36

Oh right

Answer 37

I think this might be a bit confusing because I'm telling you to do something very simple that its almost silly.

If I were to ask you to phrase "Y is always 2x" in an equation, how would you do that?

Answer 38

I would substitute 2x in for y right??

Answer 39

Im sorry im just so used to trick questions in math that when im asked to do something simple I overthink it.

Answer 40

Yeah, I get that, it's totally fair. Tell me, when can you substitute things?

Answer 41

What do you mean? I do it in equations..

Answer 42

Hm, well, if I had the equation

y = 2x

I would not be able to substitute in 3 for y and 7 for x cause that would create
3=2(7)

which isn't true.

Answer 43

So when am I "allowed" to substitute?

Answer 44

When the statement is true

Answer 45

When is the statement true?

Answer 46

When what you substituted works in the equation right?

Answer 47

Imagine you're explaining this to someone who has never seen an equation before. How would you explain to them when an equation "works?"

Answer 48

Like when the x or y is isolated right? because thats always the goal

Answer 49

So if an equation doesn't have an x or a y its not true?

What about when 2 + 3 =5

X and y aren't isolated there, is that not true?

Answer 50

No i was just trying to think of an example. That is still true. Its true when both sides are equal

Answer 51

Okay! Awesome! Perfect. So, another way of saying "two things are the same" is to say that "they are equal" right?

Answer 52

Yep!

Answer 53

Awesome, Going back, so if I asked you to express "y is the same as 2x" in an equation, how would you do that?

Answer 54

y=2x?

Answer 55

Yes! Awesome. That's exactly right. An equation is the same thing as saying that both sides are the same.

Answer 56

Now, going back to our problem, If I asked you to express "x is always the same as 1"

How would you do that?

Answer 57

Okay haha sorry that took so long its been a long day.

Answer 58

x=1

Answer 59

No its cool don't apologize, and yes! Awesome!

Now, I'm going to ask you to use the draw tool. Can you plot all of the points (or at least, a few of them) where x =1?