MASTERSHEET 
Copy/Paste Formulae for Chapter 1 Linear Relations Chapter 2 Coordinate Geometry

>Copy the formula you need
>Paste it into the other workbook you are using
>NOTE: Do NOT alter the formulae in this workbook, these are your templates only.

Handy Shortcuts

Shift+Enter to execute a command
Ctrl-s save your file
Alt+7 to start a text cell
Ctrl-/ gives a fraction (□/□)
Ctrl-2 gives a square root sign (Sqrt[□])
Ctrl-6 gives an exponent (□^□)

All Mathematica commands start with a Capital and use square brackets [ ]
For examples Plot [ ]

MATHEMATICA COMMANDS FOR Chapter 1 &2

1. Solve Equations

Solve["Left side of Equation"=="Right side of Equation","solve for"]

Solve[2x==8,x]//N

2. Solve Simultaneous Equations

Solve[{equation here number one,another equation here},{variable1,variable2}]

Solve[{2x+3y==6,x-2y==4},{x,y}]//N

3. Find x-intercepts,  y-intercepts of a line , Transfer to Gradient Y-Intercept Form and then plot the line

lm=Solve["Left side of Equation"=="Right side of Equation",y]/.x->0
Print["Y-intercepts",Normal[lm]]
lm=Solve["Left side of Equation"=="Right side of Equation",x]/.y->0
Print["X-intercepts",Normal[lm]]
lm=Solve["Left side of Equation"=="Right side of Equation",y]//Expand
Print["Gradient Y-intercept form->", Normal[lm]]

Plot[1-(x/2),{x,"Minimum","Maximum"}]

lm=Solve[y==2x-10,y]/.x->0
Print["Y-intercepts",Normal[lm]]
lm=Solve[y==2x-10,x]/.y->0
Print["X-intercepts",Normal[lm]]
lm=Solve[2x+4y==4,y]//Expand
Print["Gradient Y-intercept form->", Normal[lm]]

Plot[1-(x/2),{x,-10,10}]

4. Length between two points

(Sqrt[((((Subscript[x, 2])-((Subscript[x, 1]))))^2)+((((Subscript[y, 2])-((Subscript[y, 1]))))^2)])

EuclideanDistance[{(Subscript[x, 1]),(Subscript[y, 1])},{(Subscript[x, 2]),(Subscript[y, 2])}]

EuclideanDistance[{-1,-4},{3,4}]

5. Midpoint between two points

{(((Subscript[x, 1])+((Subscript[x, 2])))/2),(((Subscript[y, 1])+((Subscript[y, 2])))/2)}

Midpoint[{{(Subscript[x, 1]),(Subscript[y, 1])},{(Subscript[x, 2]),(Subscript[y, 2])}}]

Midpoint[{{-1,-4},{3,4}}]

6. Point Gradient Form :  y-(Subscript[y, 1])=  m(x-(Subscript[x, 1]))

Solve[y-((Subscript[y, 1]))==m(x-((Subscript[x, 1]))),y]

7. Given two points to find equation

m:=(("\!\(\*SubscriptBox[\(y\), \(2\)]\)"-("\!\(TraditionalForm\`\*SubscriptBox[\(y\), \(1\)]\)"))/("\!\(\*SubscriptBox[\(x\), \(2\)]\)"-("\!\(TraditionalForm\`\*SubscriptBox[\(x\), \(1\)]\)")))
Solve[y-"\!\(TraditionalForm\`\*SubscriptBox[\(y\), \(1\)]\)"==m(x-"\!\(TraditionalForm\`\*SubscriptBox[\(x\), \(1\)]\)"),y]//Expand

m:=((2-(-2))/(3-(1)))
Solve[y--2==m(x-1),y]//Expand

8. To plot one graph

Plot[{"function"},{x,"Minimum","Maximum"},PlotLegends->"Expressions"]

Plot[{2^x},{x,0,10},PlotLegends->"Expressions"]

9. To plot few graphs on the same plane

Plot[{"function1","function2","function3"},{x,"Minimum","Maximum"},PlotLegends->"Expressions"]

Plot[{Sin[x],Sin[2x],Sin[3x]},{x,0,2Pi},PlotLegends->"Expressions"]

10. Solve Inequalities

Reduce["Left side of the inequality""inequality sign here""Right side of the inequality","solve for",Reals]

Reduce[(72+15z)/3>4,z,Reals]

11. Plot The line with gradient m and y-axis intercept c

12. Plot The line with any given points

13. Parallel Lines

14. Perpendicular Lines