1. Heart of Algebra Lessons 3 & 4
Creating, Evaluating, and Interpreting Linear Functions
Finding Slope
Slope of Parallel and Perpendicular Lines
Solving Systems of Linear Equations
Solving Systems of Linear Inequalities

2. Creating, Evaluating, and Interpreting Linear Functions
Creating a Linear function means writing an equation in the form y = mx + b
The variable goes with the repeated element, watch for words like “per” and “each”
Evaluating a function means plugging in the number for the variable and getting a number answer
Interpreting a function means finding what the slope and y-intercept stand for in the story

3. Finding Slope
If given an equation, rewrite in y = mx + b form: “m” is the slope. Do not include x!
If given two points use the formula
𝑚= 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1
If given a graph, you can count the slope
𝑚= 𝑟𝑖𝑠𝑒 𝑟𝑢𝑛

4. Slope of Parallel and Perpendicular Lines
Parallel Lines never touch so they must be slanted the same direction and the same amount, thus Parallel Lines have Equal Slopes
Perpendicular Lines meet at a right angle so they must be slanted opposite directions, thus Perpendicular Lines have Opposite Reciprocal Slopes Ex) ⅓ and -3

5. Solving Systems of Linear Equations
Three methods to solve
Graphing: Must get both equations in y = mx + b form
Substitution: Isolate one letter then plug that expression into the other equation
Elimination: Add or Subtract the two equations to eliminate one of the letters *May need to multiply
Since some of the test is multiple choice you can guess and check the answers
Remember the solution must work in BOTH equations

6. Solving Systems of Linear Inequalities
Graph each boundary line and shade on the appropriate side
The answers are in the region that is shaded twice (dark)
For multiple choice – guess and check to find the point that works in BOTH inequalities