Unit 2 Test Study Guide: Linear Functions and Systems
Linear functions and systems are essential topics in algebra because they describe relationships that change at a constant rate. This unit 2 test study guide covers the concepts and problem-solving methods you need to master, including slope, equations of lines, graphing, systems of equations, inequalities, and common applications in real-world situations.
What Is a Linear Function?
A linear function is a function that can be written in the form
[ f(x)=mx+b ]
or
[ y=mx+b ]
where:
- (m) is the slope, or constant rate of change
- (b) is the (y)-intercept
- (x) is the independent variable
- (y) is the dependent variable
The graph of a linear function is a straight line. The slope tells you how much (y) changes for each unit increase in (x), while the (y)-intercept tells you where the line crosses the (y)-axis Less friction, more output..
Here's one way to look at it: consider the function
[ y=3x-2 ]
The slope is (3), and the (y)-intercept is (-2). To graph it, plot ((0,-2)). Plus, then move one unit to the right and three units up to reach ((1,1)), followed by two units right and six units up to reach ((2,4)). Drawing a straight line through these points gives the graph Most people skip this — try not to. Less friction, more output..
No fluff here — just what actually works.
Understanding Slope
The slope of a line measures its steepness and direction. It can be calculated from two points on the line:
[ m=\frac{y_2-y_1}{
