Formula: m = Rise (vertical)/Run (horizontal)
m = (y2 - y1) / (x2 - x1)

Line that goes up to right is positive slope
Line that goes down to left is positive slope
Line that goes up to left is negative slope
Line that goes down to right is negative slope

Parallel: Slope = same, y-intercept = different (Symbol ∥)

To write any equation, need slope and a point on line

Both A and B cannot be zero
A is a whole number (not fraction)

Horizontal line equation: y = value (x ∈ R, slope = 0)
Vertical line equation: x = value (y ∈ R, slope = undefined)

General form: if A > 0, B > 0, C > 0, then: negative slope
negative y-intercept
negative x-intercept

Number pattern increasing or decreasing at a constant rate

2, 4, 8, 16, 32.... (not an arithmetic pattern)

1. Equation: tn = dn + a
2. Plot y-intercept (a)
3. Use slope (d) = rise/run to get next point
4. Continue plotting rest of points
5. Do NOT join points into line because n is only natural numbers
6. Remove y-intercept because n CANNOT be zero

1. Linear: y-intercept; arithmetic: NO y-intercept
2. Linear: continuous, infinite points; arithmetic: no line, distinct points

Ordered pair that satisfies both equations is the solution of the system

Find solution: graph the two lines and the point of intersection is the solution

Parallel lines have NO SOLUTION because they cannot intersect - inconsistent system

Lines have same slope, same y-intercept, then infinite solutions - consistent system

Lines have different slope, then ONLY ONE solution - consistent system

If the x or y variables differ in signs, eliminate through ADDITION

If x or y variables are exactly the same, eliminate through SUBTRACTION

If you multiply linear equation by constant, does not change the solution

1. Using equation with variable that has coefficient of 1, solve that variable
2. Substitute that solution in the other equation

-n^m = always negative
(-n)^m = if m is odd, answer is negative. If m is even, answer is positive.

Multiplying powers /w same base= add exponents
Ex. n^m x n^p = n^(m + p)

Dividing powers /w same base = subtract exponents
Ex. n^m ÷ n^p = n^(m - p)

Negative exponent in the numerator: bring to denominator to make it positive
Negative exponent in the denominator: bring to numerator to make it positive

Domain: first set of elements (Surrey, BC), x value(s)

Range: second set of elements (Surrey, BC), y value(s)

*Do not repeat listing of same number in domain or range

A relation with ordered pairs graphed in a straight line

Values of x and y increase/decrease by a constant amount

1. Degree of equation = 1 (NO x^2 + y^2)
2. Variables cannot multiply (NO xy)
3. Variables cannot be in denominator (NO y = 7/x+3)
4. Variables cannot be exponent (NO y = 7^x)

Each element in domain is associated with EXACTLY one element in range

Tip: in a table, if any X (domain) value repeats, it is NOT a function

Tip: in a graph, any two points on same x axis, is NOT a function
Any points joined by vertical line, is NOT a function

1. Arrows = line extends
2. Solid dot = end point
3. Outlined dot = approaching, but NOT REACHING end point

Inequality symbols
greater than: >
less than: <
greater than or equal to: ≥
less than or equal to: ≤

Tip: Smaller number then variable then larger number
Tip: always read from variable to the number

Ex. A range of numbers greater than -2 = (-2,∞)

Ex. y is an element of real numbers such that y is greater than -2 = {y | y > -2, y ∈ R}

There is a simplified option = y > -2

To find y intercept, put x = 0
To find x intercept, put y = 0
Graph the equation using x and y intercepts

Input values are independent variables (x)
Output values are dependent variables (y)

Discrete data = points NOT connected in graph (integers)
Continuous data = points connected in graph (real numbers)

Rate of change = change in dependent variable ⁄ change in independent variable
Also known as... Slope = rise ⁄ run

If bases are the same, then exponents are the same
Ex.5^(x+4) = 5^(-2), so x+4 = -2

General rule of fractional exponents: numerator is the power and the denominator is the root.
We can write x^(m/n) as n√(xm)

To simplify radical form, multiply numerator and denominator by the root because you cannot have root in denominator