Download Algebra I Study Guide for EOCE

Graphing:
3 methods
1 – table (use at least 3 points, 5 is better)
2 – intercepts (be careful - only 2 points, one where x = 0 and one where y = 0)
3 – y = mx + b (best method)
m = slope = rise
run
b = y-intercept (the starting point)
Positive slope
Zero slope
Negative Slope
Undefined Slope (or no slope)
A line with a slope of “0” has a slope. An undefined line does not have a slope.
Horizontal Line → zero slope → y = constant (Ex: y = 7)
Vertical Line → undefined (or no) slope → x = constant (Ex: x = -4)
Parallel lines have the same slope.
Perpendicular lines have slopes that are opposite reciprocals (2/3 and -3/2).
Ex: Find the slope of the line containing the points (2, 3) and (-4, 1).
2 ways – graph and count OR use formula
∆y = (y1 – y2) = (3 – 1) = 2 = 1
∆x (x1 – x2) (2 – -4) 6 3
(Remember that it doesn’t matter what order you choose the y’s, as long as you choose the x’s in the same order.)
Solving Systems: (3 methods)
1 - graphing (find the point/area of intersection – the only method you can use for solving systems of
inequalities)
2 - substitution (if you already have one equation in the form of “x =” or “y =” or if you can get them in
that form easily)
3 - elimination/linear combinations (if you notice that the coefficients of either x or y are opposites; this is
the method that can be used for all systems of equations)
Exs:
Substitution
2x + 3y = 12
2(y + 1) + 3y = 12
x = 2 +1
x=y+1
2y + 2 + 3y = 12
x=3
5y + 2 =12
-2 -2
5y = 10
(3, 2)
5 5
y=2