Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I'm taking Algebra II, and I need help on two types of problems. The numbers may not work out, as I am making these up. 1st problem example: Using the following functions, write a linear functions. f(2) = 3 and f(5) = 4 2nd problem example: Write a solution set for the following equation (I thought you couldn't solve a linear equation?) 2x + 4y = 8 Feel free to use different numbers that actually work in your examples, these problems are just making me scratch my head.

share|cite|improve this question
up vote 2 down vote accepted

First problem. At this level, a "linear function" is one of the form $f(x) = ax+b$ for some $a$ and $b$

If you know that $f(2)=3$ and $f(5)=4$, then by plugging in you get two equations: $$\begin{align*} 3 &= 2a + b\\ 4 &= 5a + b \end{align*}$$ From these two equations, you should be able to solve for $a$ and $b$, thus finding the function. For example, you can solve for $b$ in the first equation, substitute in the second, and solve the resulting equation for $a$; then plug that to find the value of $b$.

Second Problem. An equation like $2x+4y = 8$ does not have a unique solution, but each value of $x$ gives you a corresponding value of $y$ and vice-versa. The "solution set" of this would be a description of all the values that make the equation true.

For instance, if you had the problem "Write a solution set for $x-3y=4$", you could do the following: given a value of $y$, the value of $x$ has to be $4+3y$. So one way to write the solutions is: $$\bigl\{ (4+3y, y)\,\bigm|\, y\text{ any real number}\bigr\}.$$ For each real number $y$, you get one solution.

Or you could solve for $y$, to get that $y=\frac{x-4}{3}$, and write a solution set as: $$\left\{\left. \left(x, \frac{x-4}{3}\right)\,\right|\, x\text{ any real number}\right\}.$$

share|cite|improve this answer
Thanks, this is just what I needed! – Luke Milse Sep 9 '11 at 4:24

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.