Fitting Plot onto TikZ Coordinate Plane

Question

I am trying to create simple worksheets where students either: (a) see a randomly generated linear graph and must determine the equation or (b) are given a randomly generated linear equation and must plot the line.

How do I make the graph stay on the given portion of the plane? i.e. from -10 to 10 for both x and y.

Is there some "easy" way to do it, or do I have to use a formula that relates the randomly generated slope \m and y-intercept \b to an appropriate domain or range?

\documentclass{article}

\usepackage{pgf}
 \pgfmathsetseed{\number\pdfrandomseed}
\usepackage{tikz}

\pagestyle{empty}

\begin{document}


\newcommand{\LinearEquation}
{%
%slope
\pgfmathsetmacro{\m}{int(random(0,8)-4)}%

%y-intercept
\pgfmathsetmacro{\b}{int(random(0,8)-4)}%

% Linear Equation
\(y={\m}x+\b\)
}
\LinearEquation


\begin{tikzpicture}[scale=0.3]
\draw[help lines, gray, thin] (-10,-10) grid (10,10);
\draw[very thick,<->] (-10.3,0)--(10.3,0);
\draw[very thick,<->] (0,-10.3)--(0,10.3);
\draw[red, very thick, , range=-10:10, <->] plot (\x,\m*\x+\b); %this did not work
\end{tikzpicture}

\end{document}

Answer 1

Assuming you don't need the arrow tips for the line, just add \clip (-10,-10) rectangle (10,10); before you plot. And in the options for the plot, you want domain, not range.

Note also that \b is already defined (see Short names for macros), so it's best to avoid using it.

\documentclass{article}
\usepackage{tikz}
 \pgfmathsetseed{\number\pdfrandomseed}

\pagestyle{empty}
\newcommand{\LinearEquation}
{%
%slope
\pgfmathsetmacro{\Slope}{int(random(0,8)-4)}%

%y-intercept
\pgfmathsetmacro{\Intercept}{int(random(0,8)-4)}%

% Linear Equation
\(y={\Slope}x+\Intercept\)
}

\begin{document}
\LinearEquation

\begin{tikzpicture}[scale=0.3]
\draw[help lines, gray, thin] (-10,-10) grid (10,10);
\draw[very thick,<->] (-10.3,0)--(10.3,0);
\draw[very thick,<->] (0,-10.3)--(0,10.3);
\clip  (-10,-10) rectangle (10,10);
\draw[red, very thick, , domain=-10:10] plot (\x,\Slope*\x+\intercept); 
\end{tikzpicture}
\end{document}

Everything in one macro

\documentclass{article}
\usepackage{tikz}
 \pgfmathsetseed{\number\pdfrandomseed}

\pagestyle{empty}
\newcommand{\LinearEquation}
{%
%slope
\pgfmathsetmacro{\Slope}{int(random(0,8)-4)}%
%y-intercept
\pgfmathsetmacro{\Intercept}{int(random(0,8)-4)}%
\begin{tikzpicture}[scale=0.25]
\draw[help lines, gray, thin] (-10,-10) grid (10,10);
\node [above right] at (-10,10) {\(y={\Slope}x+\Intercept\)};
\draw[very thick,<->] (-10.3,0)--(10.3,0);
\draw[very thick,<->] (0,-10.3)--(0,10.3);
\clip  (-10,-10) rectangle (10,10);
\draw[red, very thick, , domain=-10:10] plot (\x,\Slope*\x+\Intercept); 
\end{tikzpicture}%
}

\begin{document}
\LinearEquation
\LinearEquation

\LinearEquation
\LinearEquation

\LinearEquation
\LinearEquation

\end{document}