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Linear Relationships Cheat Sheet by

MATHSSSSSSSSSSSSSSSSSSSSS

Formulas

Straight Line
y=mx+c
Equation of parallel line OR Point of inters­ection
y-y1­=m(­x-x1)
Midpoint
([x1­+x­2/­2],­[y­1+­y/2])
Distance Formula
√(x2­-x­12­+(y­2­-y­1)2
Gradient of parallel line
m1=m2
Gradient of perpen­dicular line
m1m­2=-1 OR m2=-­1/m1 & -m2=­1/m1
Gradient
m=rise/run OR m=(y-y­1­)/(­x-x1)
 

Solving Stuff

Finding a rule for a graph
For: (x1,­y1) & (x2,­y2) Find gradient Sub into y-y1­=m(­x-x1)
Finding equation of parallel line
Arrange into y=mx+c Find values of x,y,m Sub into y-y=m(x-x) Solve
Finding equation of perpen­dicular line
Find negative reciprocal of m Substitute (x,y) into y=mx+c Solve for c
Finding point of inters­ection
Arrange one of the lines into y=mx+c or x= Sub this into the other line Solve for other coordinate
Shading Half Planes
>above <below
Horizontal Line
y=b
Vertical Line
x=a
Forming Simult­aneous Equations
Define unknowns using pronum­erals. Form two equations from the inform­ation in the problem. Solve simult­ane­ously. Answer the question in words.
Solving Simult­aneous
Solve two equations in two pronum­erals using: substitution when one pronumeral is the subject; e.g. y = x + 4. elimination when adding or subtra­cting multiples of equations eliminates one variable.
If asking for 'through (x,y) perpen­dicular to x=a, answer y=b e.g perp. tp x=7 through (0,3) = y=3
           

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