Linear Relationships Cheat Sheet

Straight Line	y=mx+c
Equation of parallel line OR Point of intersection	y-y¹=m(x-x¹)
Midpoint	([x¹+x²/2],[y¹+y²/2])
Distance Formula	√(x²-x¹)²+(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=(y²-y¹)/(x²-x¹)

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

Linear Relationships Cheat Sheet by maxine3