# General Graphing

I'd like to create a general graph to illustrate a point (ex. mx+b and show b is intercept and m is slope). I understand that I can create a graph with manual axis naming, but I'd like to also be able to position a label b at the intercept, label a couple of points and label m as the slope. I understand I may have to input unrelated integer values, but the labeling is what matters.

As an added bonus, I would also want to be able to show how I can adjust certain features and the line would change. (perhaps also a label on the arrow but I forgot to include that in the sketch)

I have attached a couple quick sketchs of the general idea below for clarity. How would I achieve this?

• Your pictures are difficult to understand for myself. – user213378 Sep 21 '20 at 8:55
• @TrongVuong1998 - what part is difficult to understand? – user209429 Sep 21 '20 at 15:55

An alternative in Metapost wrapped up in luamplib. Compile this with lualatex.

Follow the link above for tutorials and manuals that explain how MP works.

\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
numeric u, m, m', b, b';
u = 1.44cm;
b = 3.6u;  b' = b + 7/8 u;
m = -1;  m' = 7/8 m;

path xx, yy;
xx = (left -- 5 right) scaled u;
yy = xx rotated 90;

numeric minx, maxx; path ff, gg;
minx = xpart point 1/16 of xx;
maxx = xpart point 15/16 of xx;
ff = (minx, minx * m + b) -- (maxx, maxx * m + b);
gg = (minx, minx * m' + b') -- (maxx, maxx * m' + b');

z0 = point 0.4 of ff;
z1 = point 0.54 of ff;
z1 0 = whatever [point 0 of gg, point 1 of gg]; x1 0 = x0;
z1 1 = whatever [point 0 of gg, point 1 of gg]; x1 1 = x1;

forsuffixes @=0, 1:
draw (x@, 0) -- z@ -- (0, y@) dashed evenly scaled 3/4;
draw z@ -- z1 @ -- (0, y1 @) dashed withdots scaled 1/2;
label.bot("$x_{" & decimal @ & "}$", (x@, 0));
label.lft("$y_{" & decimal @ & "}$", (0, y@));
label.lft("$y'_{" & decimal @ & "}$", (0, y1 @));
endfor

draw ff withcolor 2/3 red;
draw gg withcolor 3/4 blue;
drawarrow xx; drawarrow yy;

label.rt("$x$", point 1 of xx);
label.top("$y$", point 1 of yy);

dotlabel.urt("$b$", (0, b));
dotlabel.urt("$b'$", (0, b'));

draw thelabel("slope: $m=" & decimal m & "$", 7 up)
rotated angle (1, m) shifted point 2/3 of ff;
draw thelabel("slope: $m'=" & decimal m' & "$", 7 up)
rotated angle (1, m') shifted point 2/3 of gg;

endfig;
\end{mplibcode}
\end{document}


The syntax to get the y' points is a bit tricky; but MP allows spaces between elements of a variable suffix so z0 1 is a valid name for a variable, and the usual z macro magic, means that x0 1 and y0 1 refer to the x and y parts as usual.

• Would it be possible to add the arrow or does that become extremely difficult? Would you happen to know if it is possible to run this on Overleaf? – user209429 Sep 21 '20 at 16:13
• No, an arrow is really easy... – Thruston Sep 21 '20 at 16:13
• And yes you can run this on Overleaf -- just be sure to choose lualatex as the formatting engine in the options. – Thruston Sep 21 '20 at 16:14
• How would I add the arrow and vertical shift the labels? The labels are touching the line they are labeling which I would prefer to avoid. – user209429 Sep 21 '20 at 17:01
• If you want to make changes, then I suggest that you read the tutorials and manuals that you can find at the link at the top of my answer. – Thruston Sep 21 '20 at 19:39

For a starting point and only for first image.

\documentclass[margin=3mm]{standalone}
\usepackage{tikz}

\newcommand{\LinearEquation}
{%
\pgfmathsetmacro{\Slopef}{-1}% slope of the line 1
\pgfmathsetmacro{\Interceptf}{6}% intercept
\pgfmathsetmacro{\Slopes}{-0.9}% slope of the line 2
\pgfmathsetmacro{\Intercepts}{5}% intercept
\begin{tikzpicture}[>=latex]
\draw[->] (-1,0)--(8.3,0)node[below]{$x$};
\draw[->] (0,-1)--(0,8.3)node[left]{$y$};
\draw[very thick,red, domain=0:5] plot (\x,\Slopef*\x+\Interceptf);
\node at (0,\Interceptf)(b)[left]{$b$} ;
\def\x1{1.5}
\def\y1{\Slopef*\x1+\Interceptf}
\draw [dashed,blue](\x1,0)node[below]{$x1$}--(\x1,\y1)--(0,\y1)node[left]{$y1$};
\def\x2{3}
\def\y2{\Slopef*\x2+\Interceptf}
\draw [dashed,blue](\x2,0)node[below]{$x2$}--(\x2,\y2)--(0,\y2)node[left]{$y2^\prime$};

\draw[very thick,red, domain=0:5] plot (\x,\Slopes*\x+\Intercepts);
\node at (0,\Intercepts)(b)[left]{$b$} ;
\def\x1{1.5}
\def\y1{\Slopes*\x1+\Intercepts}
\draw [dashed,blue](\x1,0)node[below]{$x1$}--(\x1,\y1)--(0,\y1)node[left]{$y1^\prime$};
\def\x2{3}
\def\y2{\Slopes*\x2+\Intercepts}
\draw [dashed,blue](\x2,0)node[below]{$x2$}--(\x2,\y2)--(0,\y2)node[left]{$y2$};
\draw [<-](2.8,3.5)--(5,3.5)node[right]{Slope $m$};
\draw [<-](2.9,2.5)--(5,2.5)node[right]{Slope $m^\prime$};
\end{tikzpicture}%
}

\begin{document}
\LinearEquation
\end{document}


• How would one add another line to this? Would there be any way of doing this within the document itself and not setting the specific image as a command? – user209429 Sep 21 '20 at 16:11
• @user760900, I have edited my answer. You can insert this file using standalone package. – ferahfeza Sep 21 '20 at 17:04