You will want to refer to Year 8 Maths Chapter 7 for basic linear relationships. This section is more advanced, and omits basic concepts.
- Gradient-intercept form
- General Form
- Distance formula
- Direct proportion/direct variance
- Parallel lines and perpendicular lines:
y = 0 y-intercept =
x = 0 ***
The gradient is a measure of slope.
rise Gradient = –––––– run
Be careful when the gradient is negative.
y = mx + b
m is the gradient, and
b is the y-intercept. ***
ax + by = c
ax + by + c = 0
where a, b and c are constants. It is typically the result of an expanded FOIL. ***
The midpoint is the halfway point between two end points. To find the midpoint, use the midpoint formula.
┌ x1 + x2 y1 + y2 ┐ M = | ––––––– , ––––––– | └ 2 2 ┘
x coordinate is the average of the two
x coordinates The
y coordinate is the average of the two
To find a length of a line, use Pythag.
Alternatively, use the Distance Formula.
___________________________ d = √ (x2 - x1)^2 + (y2 - y1)^2
_______________________________ d = √ ((-7) - (-3))^2 + ((-4)-2)^2 _________________ d = √ (-4)^2 + (-6)^2 d = √52 d = 2√13 d = 7.21 units (2dp)
If b is directly proportional to a:
b = ka
where k is a constant.
Also known as:
y = mx
If two lines are parallel they have the same gradient. If two lines are perpendicular (at right angles) then they are reciprocals of each other.
Let the gradients of two perpendicular lines be m1 and m2. m1 x m2 = -1 1 m2 = ––– m1 Hence, m2 is equal to the reciprocal of m1