# General form of an equation with undefined slope

1. Sep 3, 2017

### Orson

1. The problem statement, all variables and given/known data
The equation of the line that goes through the points and can be written in general form . What are the values for A, B, and C?

2. Relevant equations
Ax+By+C=0

3. The attempt at a solution
I think the answer is x=1. But how do i express that in general form?

Last edited by a moderator: Sep 3, 2017
2. Sep 3, 2017

### Staff: Mentor

As x - 1 = 0.
In this form, A = 1. Can you figure out what B and C are?

3. Sep 3, 2017

### Orson

The software says A=1 is wrong.

4. Sep 3, 2017

### Orson

I just found out how to do it. Pretend you're trying to figure out the slope. you get 4/0 . 4 is the value for A. 0 for B. solve for c.

A= 4
B= 0
C= -4

5. Sep 4, 2017

### SammyS

Staff Emeritus
Does the software mark A, B, and C individually or does it mark them together as a group of numbers ?

Last edited: Sep 4, 2017
6. Sep 4, 2017

### Orson

Individually.
A= blank. B=blank. C=blank

7. Sep 4, 2017

### MarkFL

I recommend reviewing post #2 to get the line in the given general form...

8. Sep 4, 2017

### SammyS

Staff Emeritus
I take that the software says those answers are correct.

As it turns out there are infinitely many correct solutions. (You might say, infinitely many.)

The only one of the three which must have a particular value is B, which is zero.

The only requirements on A and C is that A = −C , so that A + C = 0 .

9. Sep 4, 2017

### Orson

I am pretty sure at one point I had 1 and -1 for a and c and software marked it wrong. Grrrrrr.

10. Sep 4, 2017

### Orson

I plugged 4 in for A and 0 for B because I read somewhere you act like you're going to figure the slope out (even though you can't) in order to get A and B.

11. Sep 4, 2017

### Nidum

Rewrite the equation in slope and intercept form : y = mx + d

Sketch the graph of the line .

Is there something about the coordinate values given for those two points on the line that might cause you to think about this problem in a particular way ?

Last edited: Sep 4, 2017
12. Sep 4, 2017

### SammyS

Staff Emeritus
Using that same idea, you can just as well get A = −4, B = 0, and C = 4 , by using the coordinates in the reverse order.

13. Sep 4, 2017

### Orson

Yes. I see how infinitely many solutions are possible for a and c. I put the equation in
Yes. I see you can put any number and its complement to make b 0. I also solved for x and got x=1 which makes sense. How would i get the equation for a vertical line at 2?

14. Sep 4, 2017

### Orson

They form a straight vertical line?

15. Sep 4, 2017

### Orson

Also, I converted it to slope intercept form. I get 0=-4x+4. Is that what you're getting at?

16. Sep 4, 2017

### Orson

Or simply y=-4x+4?

17. Sep 4, 2017

### SammyS

Staff Emeritus
So you want an equation of the form $\ Ax+By+C = 0\$ that with suitable values for A, B, C is equivalent to the equation $\ x=2\ .$

$\ x=2\$
is equivalent to
$\ x-2=0\ .$
Multiplying by A and adding $\ 0y\$ gives
$\ Ax+0y-2A=0\ .\$ (Solve it for x to convince yourself.)

So B = 0, and you can choose any non-zero number for A (you need x in the equation). Then C is −2 times the value chosen for A.

Otherwise, to do it by your method:
Pick any two distinct points, both having 2 for the x coordinate and proceed.

18. Sep 4, 2017

### epenguin

Now you have got what Nidum #10 hinted. You could have said at the start: to one x value corresponds two y values; for a straight line that can only be a vertical line.
Sure you copied out the question right?

Last edited: Sep 5, 2017
19. Sep 4, 2017

### Orson

I am sure I copied the question right. Thanks.

20. Sep 4, 2017

### epenguin

So in conclusion what is the equation of the line in simplest form?

21. Sep 4, 2017

### Orson

simplest form, I would say x=1. I am heeding what it says in your sig.