how to write an equation and graph it given only one point on the line

allegansveritatem

Full Member
The instructions for this problem are: Given the ordered pair (1.3) write an equation for the line and graph it. I came up with this: x +y= 4. The answer at the back of the book is: x= y-2. Why is the one correct and the other not? They can't both be right because they graph two different slopes.

There is something very elementary here that I am missing. I almost know what it is but can't quite express it.

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JeffM

Elite Member
The instructions for this problem are: Given the ordered pair (1.3) write an equation for the line and graph it. I came up with this: x +y= 4. The answer at the back of the book is: x= y-2. Why is the one correct and the other not? They can't both be right because they graph two different slopes.

There is something very elementary here that I am missing. I almost know what it is but can't quite express it.
The problem AS YOU HAVE GIVEN IT makes no sense. It takes two points to determine a line. Please give the wording of the problem exactly and completely. There are an infinite number of lines which include (1, 3).

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Dr.Peterson

Elite Member
The instructions for this problem are: Given the ordered pair (1.3) write an equation for the line and graph it. I came up with this: x +y= 4. The answer at the back of the book is: x= y-2. Why is the one correct and the other not? They can't both be right because they graph two different slopes.

There is something very elementary here that I am missing. I almost know what it is but can't quite express it.
What's missing is the rest of the problem.

If all they gave you was one point, (1,3), and they didn't mention a slope, then both answers are correct, and it is improper for the exercise to call it "the line".

Did you quote the entire problem? Perhaps this was part of a series of exercises, for which there were some common instructions you have missed?

Am I right, though, that it said (1,3) and note (1.3), which is not an ordered pair?

allegansveritatem

Full Member
What's missing is the rest of the problem.

If all they gave you was one point, (1,3), and they didn't mention a slope, then both answers are correct, and it is improper for the exercise to call it "the line".

Did you quote the entire problem? Perhaps this was part of a series of exercises, for which there were some common instructions you have missed?

Am I right, though, that it said (1,3) and note (1.3), which is not an ordered pair?
Yes, you're right. It was a typo on m y part.
The exact wording is: "Write a linear equation in two variables that has (1,3) as one of its solutions. Then graph the equation." Since this is an even numbered problem the answer is not given...I said it was in my post but I was speaking from memory and now that I have the book (it was out in the car) I see that no answer was given. My answer is: x+y=4 I doubt that is right however because another problem similar to this for which I got a similar answer had an official back-of-the-book solution that was much other than mine. So..is this problem solvable with the information supplied?

mmm4444bot

Super Moderator
Staff member
… Write a linear equation in two variables that has (1,3) as one of its solutions. Then graph the equation.

… My answer is: x+y=4
That's one of many possible answers.

So is: 3x = 2 + y/3 :cool:

Did you graph x + y = 4?

allegansveritatem

Full Member
That's one of many possible answers.

So is: 3x = 2 + y/3 :cool:

Did you graph x + y = 4?
yes. The line crossed the x axis at 4 and the y axis at 4. I am beginning to think that the problem was seeking any one of an infinite number of possible equations. No? But this sort of problem was not covered in the chapter so I thought one and only one solution was desired.

mmm4444bot

Super Moderator
Staff member
As it's worded, yes, there are infinite possible answers. The book gives a specific answer, so there could be a typo in the exercise statement.

JeffM

Elite Member
Yes, you're right. It was a typo on m y part.
The exact wording is: "Write a linear equation in two variables that has (1,3) as one of its solutions. Then graph the equation." Since this is an even numbered problem the answer is not given...I said it was in my post but I was speaking from memory and now that I have the book (it was out in the car) I see that no answer was given. My answer is: x+y=4 I doubt that is right however because another problem similar to this for which I got a similar answer had an official back-of-the-book solution that was much other than mine. So..is this problem solvable with the information supplied?
Look closely at the language of the problem. "A linear equation" does not imply that there is only one possible answer. To imply a singular answer would require a definite article, "the," rather than the indefinite article of "a."

You can answer the question, but there is not a unique answer. Your answer is one of the correct answers because x = 1 and y = 3 does entail that 4 = x + y = 1 + 3. It is possible that your book wants you to write that equation in a different form such as y = 4 - x.

Because you have not told us what the other problem was, or what your answer was, or what the book's suggested answer was, it is utterly impossible for us to comment on the other problem. It is possible that the book's answer is a misprint (it happens) or that the two problems are fundamentally different. How can we know unless we know the problem and at least your answer?

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tkhunny

Moderator
Staff member
y = mx + b

3 = m(1) + b

b = 3 - m

y = mx + (3-m)

y = m(x-1) + 3 <== Pick ANY Real Value for m and you have a correct solution as stated.
Pick m = -1 and you have your initial solution.
Pick m = 1 and you have the book's solution.

Add on x = 1 and you have them ALL - infinitely many.

allegansveritatem

Full Member
Look closely at the language of the problem. "A linear equation" does not imply that there is only one possible answer. To imply a singular answer would require a definite article, "the," rather than the indefinite article of "a."

You can answer the question, but there is not a unique answer. Your answer is one of the correct answers because x = 1 and y = 3 does entail that 4 = x + y = 1 + 3. It is possible that your book wants you to write that equation in a different form such as y = 4 - x.

Because you have not told us what the other problem was, or what your answer was, or what the book's suggested answer was, it is utterly impossible for us to comment on the other problem. It is possible that the book's answer is a misprint (it happens) or that the two problems are fundamentally different. How can we know unless we know the problem and at least your answer?
You are right. I don't have the book handy right now--it is about 2 am and the book is in the car. I will get book tomorrow, copy the problem and upload it.

allegansveritatem

Full Member
The problem in question is this: Write an equation in two variable that has (2,1) for one of its solutions and then graph the equation. The answer given in back of book is:y=x-1. Then it says, and this is key and I am afraid I didn't see it the first time around: Answers may vary.

Now, the intercepts for this equation are different from those of the equation x +y= 3. So...what to make of that?

lev888

Full Member
Now, the intercepts for this equation are different from those of the equation x +y= 3. So...what to make of that?
Different lines - different intercepts.