Website for plotting many linear equations

Question

I am trying to find a site where I can paste a bunch of lines of form $y=mx+b$ and see them in a single graph. Wolfram Alpha has very limited space to do this, and other sites require that you enter things in one by one (or they only allow up to 5 or so). I have something around 50 lines.

Answer 1

Since you tagged "Linear Algebra" in your question, let's generate a coefficient matrix from a system of equations. For example if you have the 4 lines

$$ y = 3x + 2 \\ y = 4x - 1 \\ y = 6 \\ y = 2x, $$ first fill in the "missing" parts of your linear form so you explicitly have $y= mx +b$. That is, we have

$$ y = 3x + 2 \\ y = 4x - 1 \\ y = 0x + 6 \\ y = 2x + 0, $$

you would create the coefficient matrix $A$ with matrix-vector notation: $$\vec{y} = \begin{pmatrix} 3 & 2 \\ 4 & -1 \\ 0 & 6 \\ 2 & 0 \end{pmatrix} \begin{pmatrix} x \\ 1 \end{pmatrix}.$$

If you input and plot this matrix-vector product into WolframAlpha, you'll get what you need!

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Now, I imagine that you'll quickly become frustrated with having to input each entry from the coefficient matrix in the form "[[#,#],[#,#], ..., [#,#]]". But because WolframAlpha has some flexibility to it, we can transpose the system and still retain all the information to properly plot; the upside is that you would only have to enter data in the form of "[[#,#,#, ..., #], [#,#,#, ..., #]]."

Specifically, we would perform the transpose on both sides of the system to get $\vec{y}^T = (Ax)^T = x^T A^T$. Even more explicitly, we can continue working on the example given above: just be careful where you place your $m$'s and $b$'s from each $y=mx+b$!

$$ \vec{y}^T = \begin{pmatrix} x & 1 \end{pmatrix} \begin{pmatrix} 3 & 4 & 0 & 2 \\ 2 & -1 & 6 & 0 \end{pmatrix}.$$

So click here instead to see the entry in WolframAlpha, as compared to the typing necessary for the first way. Hope this helps!