Question

What is the equation of the line, in general form, that passes through the point (1, 1) and has a y-intercept of 2.
It's online school. They don't explain it.

Answer 1

Do you have the Point-Slope form?

Answer 2

y=mx+b?

Answer 3

No, not quite. That's the Slope-Intercept Form.
How about the 2-point form?

Answer 4

I don't understand. Can you walk me through with steps? I really need to learn this.

Answer 5

Yes, I can, but I need to know what tools you have available to you.

You are saying that all you have is the Slope-Intercept Form?

Answer 6

All I have is the question & the multiple choice answers. I don't know what formula to use.

Answer 7

You are not answering my questions. You need to answer my questions. Telling me what you do not have is not useful.

Slope-Intercept Form

y = mx + b

Do you know what the parts mean?

m = What?
b = What?

Answer 8

I don't have anything else. I'm not really understanding what you're asking, though. I don't know what m or b means.

Answer 9

I get more and more disappointed with online courses. Very distressing.

Okay, how about the slope. Given two points, (1,1) and (0,2), can you calculate the slope of the line passing through both points?

Answer 10

x2 - x1 over y2 - y1?

Answer 11

That's the idea, but it's the ys over the xs.

Okay, let's start with that intercept.

We are given that the y-intercept is 2. This is helpful in a couple of ways. One way is that it gives us a point. A "y-intercept of 2" MEANS the point (0,2).

Do you believe?

Answer 12

Yes. So, do you want me to calculate the point?

Answer 13

No. Stay with me.

We have two points, (1,1) and (0,2). Calculate the slope. Remember, it's the y's over hte x's.

Answer 14

That's what I meant. Okay, it's 2/-1?

Answer 15

Not quite. It should be \(\dfrac{2 - 1}{0 - 1} = \dfrac{1}{-1}\) or just -1. Do you see all those pieces working together?

Answer 16

I see. Okay, what now?

Answer 17

Now, we are almost ready to write AN equation of the line.

We have the Slope-Intercept Form, y = mx + b. In this form, m is the Slope and b is the y-intercept.

Do you see that b = 2 and m = -1?

Answer 18

Yes, I see. Now, how do we write an equation of the line?

Answer 19

Do it. Make those two substitutions and we'll be close that what the problem statement has asked.

Answer 20

I don't get how to do this part.

The answers are x - y +2 = 0
x + y - 2 = 0
x - y - 2 = 0

Answer 21

Never give me the answer. Just follow the guidance.

We have the Slope-Intercept Form, y = mx + b
We have m = -1
We have b = 2

Make those substitutions in the Slope-Intercept Form and show me what you get.

Answer 22

2 = -1x + 2?

Answer 23

Why did "y" turn into 2? We're substituting ONLY m and b. Try again.

Answer 24

Y = -1x + 2?

Answer 25

Well, just for the record, it's usually considered bad form to switch between upper case and lower case. I'll let it go, this time... :-)

Slope Intercept Form of this line is: y = -x + 2

Now, we need one more piece of information. Opinions vary what "General Form" means. Does your book or notes define it as one of these?

Ax + By + C = 0

or

Ax + By = C

Answer 26

Nope. It's not telling me anything.

Answer 27

Okay, then we'll have to look at the answers and see what it wants. It look slike it is expecting EVERYTHING on the left-hand side.

We have

y = -x + 2

Add x to both sides and see if we get closer. Show me what you get.

Answer 28

y= 2 + x

Answer 29

That doesn't make any sense. Let's try that again.

y = -x + 2

Add x to both sides

y + x = -x + 2 + x

Simplify where possible

y + x = -x + x + 2
y + x = (-x + x) + 2
y + x = 0 + 2
y + x = 2

Answer 30

Okay, now?

Answer 31

We're not there yet, are we? Subtract 2 from both sides and show me what you get. BE CAREFUL!

Answer 32

x + y - 2 = 0?

Answer 33

I didn't ask you to switch x and y. Why did you do that?

Answer 34

Accident. Is it y + x - 2 = 0?

Answer 35

I'm really not an idiot. I'm just not good at math.

Answer 36

No, it was actually fine. I was just wondering if you did it on purpose. One of the requirements of "General Form" or "Standard Form" or "Normal Form" is to list x first if it exists. You did exactly the right thing.

And we have it: x + y - 2 = 0 -- This is the correct result. Go ahead and find that on the answers.

I know of no one who thinks you are an idiot or who thinks you are no good at math - except maybe you on that last one. Here's a plan. Stop saying that. Stop believing that. You'll get it. Learn to be patient. There is no need to jump, suddenly to the end of each problem. Take your time and think through it.

Good work. Hang in there!

Answer 37

Thank you so much!