Download REMINDER: Expressions versus Equations

REMINDER: Expressions versus Equations
Simplify:
2 3x

x 4
Solve:
2 3x

x 4
=2
POLYNOMIALS:
Take the form:
Where “ai” (the coefficient) is a number in some number
system and “n” is a non-negative integer.
If a0 ≠ 0 then the polynomial is referred to as a polynomial of
degree n.
Examples: 3x + 4
is a polynomial of degree 1
(Linear)
3x2 + x – 2 is a polynomial of degree 2
(Quadratic)
x6 + 4x5 – 2x2 + 3x +7
is a polynomial of
degree 6
Linear Equations
Examples :
y = 3x +4
1
x3
f(x) = 3
1
what about: y = 3 x  3 ??
1 1
this can be re-written as y = 3 x  3
where the exponent is a negative number…thus it is NOT a
polynomial.
A linear equation takes one of two forms:
The slope/y-intercept form…………..y = mx + b
The x and y represent any point on that line, the point (x,y)
The m represents the gradient (slope) of the line
B represents the y intercept (value of y when x=0)
The general equation of a line………Ax + By + C = 0
A, B, C are parameters.
(difference between a
parameter and a variable???)
(x,y) any point on the line
The slope of this line is represented by
A
B
To find the y intercept let x =0, solve for y
To find the x interecept let y = 0, solve for x
Graphing a Linear Equation.
Easiest to do by setting the equation in slope/y-intercept
form.
Y = mx+b…………..first plot the value of b then use the
slope to generate other points.
Slope =
rise y 2  y1

run x2  x1
Deriving the equation of a line. You must have at least one
known point on that line and its slope.
Given…
- 2 points
- 1 point and the slope
- The equation of a line parallel or perpendicular to the line
AND one point on the line you are trying to determine the
equation of.