Topic A: Lines & Slope
Plotting points, slope, and equations of lines.
01 — Coordinate Plane & Slope
Points & Slope
A point (x, y) means: go x steps left/right, then y steps up/down.
- Slope: how steep a line is. Rise over run.
- Slope formula: m = (y₂ − y₁) ÷ (x₂ − x₁). It's on the formula sheet!
- Positive slope: line goes up to the right. Negative goes down.
- Horizontal line: slope 0. Vertical line: undefined slope.
Example: Points (1, 2) and (3, 8): m = (8 − 2) ÷ (3 − 1) = 6 ÷ 2 = 3.
Practice — Points & Slope
Q1 · Short Answer
Find the slope through (2, 1) and (6, 9).
Q2 · Multiple Choice
A line goes down from left to right. Its slope is:
02 — Equations of Lines
Slope-Intercept Form
Most lines can be written as y = mx + b.
- m: the slope.
- b: the y-intercept, where the line crosses the y-axis.
- Point-slope form: y − y₁ = m(x − x₁). Also on the formula sheet.
- Parallel lines: same slope. Perpendicular lines: slopes multiply to −1.
Example: y = 2x − 3 has slope 2 and crosses the y-axis at −3.
Practice — Slope-Intercept Form
Q3 · Multiple Choice
What is the y-intercept of y = −4x + 7?
Q4 · Multiple Choice
Which line is parallel to y = 3x + 1?
Topic B: Functions
Function notation and reading graphs and tables.
03 — Function Basics
What Is a Function?
A function is a machine: you put in an x, and it gives back exactly one y.
- Function notation: f(x) means "the output when you put in x".
- Evaluate: f(3) means plug in 3 for x.
- Vertical line test: if any vertical line hits the graph twice, it is NOT a function.
- Tables: each x can only have one y.
Example: f(x) = x² + 1 → f(3) = 9 + 1 = 10.
Practice — What Is a Function?
Q5 · Short Answer
If f(x) = 3x − 2, what is f(4)?
Q6 · Multiple Choice
Which set of points is NOT a function?
04 — Reading Graphs
Comparing & Reading Functions
The GED often shows a graph or table and asks what it means in real life.
- Increasing: the graph goes up as you move right.
- Maximum/minimum: the highest/lowest point.
- Intercepts: where the graph crosses the axes.
- Rate of change: for a line, this is the slope. "$15 per hour" is a rate of change.
Example: A plumber charges C = 40h + 60. The 60 is the starting fee; 40 is the cost per hour.
Practice — Comparing & Reading Functions
Q7 · Multiple Choice
A taxi costs C = 2m + 3, where m is miles. What does the 3 mean?
Q8 · Short Answer
Using C = 2m + 3, how much is a 7-mile ride, in dollars?