Using Murray's post and turning it into a function you can get your graphic this way (if I am understanding what you want).
xyCoord[slope_, area_] := Module[{soln},
soln = First@Solve[1/2 x*x*slope == area && x > 0, x];
{x, 2/360 x} /. Last[soln]]
DynamicModule[{m, area, coords},
Manipulate[coords = xyCoord[m/360, area];
Show[Plot[2/360*x, {x, 0, 1850}, Axes -> {True, True},
PlotRange -> {{0, 1850}, {0, 16}}],
Plot[m/360*x, {x, 0, 1850}, PlotStyle -> {Brown, Dashed},
Axes -> {True, True}, PlotRange -> {{0, 1850}, {0, 16}}],
Graphics[Triangle[{{0, 0}, coords, {coords[[1]], 0}}]],
ListPlot[{{{270, 1.5`}, {540, 3.`}, {810, 4.5`}, {1080,
6.`}, {1350, 7.5`}, {1620, 9.`}}, {{360, 2}, {720, 4}, {1080,
6}, {1440, 8}, {1800, 10}}}, PlotStyle -> {Red, Blue},
Filling -> Axis],
PlotLabel ->
HoldForm["Plot of simple example AreaVsTime = degree"],
LabelStyle -> {GrayLevel[0]}, ImageSize -> 600,
GridLines -> {Table[i*360, {i, 10}], None},
GridLinesStyle -> Directive[Purple, Dashed, Thin], Frame -> True,
PlotRangePadding -> Scaled[0.02],
FrameTicks -> {{Table[i, {i, 0, 20, 2}],
Table[i, {i, 0, 15, 3}]}, {Table[i*360, {i, 10}],
Table[i*360, {i, 10}]}},
FrameTicksStyle -> {{Blue, Red}, {Blue, Purple}},
FrameStyle -> Directive[FontSize -> 7],
PerformanceGoal -> "Quality"], {{m, 3, "Slope adjustment"}, 0.5,
10, Appearance -> "Labeled"}, {{area, 1440, "area"}, 10, 1800,
Appearance -> "Labeled"}]]