The big picture
Two numbers, a and b. Each does one job.
| Idea | Remember | Example |
|---|---|---|
| Polynomial | A sum of terms. Each power is a whole number. | x/4 + 3 is in. 4/x + 3 is out. |
| Degree | The highest power of the letter. | x³ + 4x + 9 has degree 3. |
| Linear rule | y = ax + b. Multiply first, then add. | 12x + 30 at x = 3 gives 66. |
| A table | Equal steps in give equal steps out. | Gaps 7, 7, 7, 7 are linear. |
| A point | (input, output), in that order. | Points of a linear rule line up. |
| Slope | a is the change for each step. Its sign sets the lean. | 2x + 6 has slope 2. |
| y-intercept | b is the output at input zero. | 2x + 5 cuts the y-axis at (0, 5). |
| Limits | A rule fits only while its answers make sense. | 100 − 20t stops at day 5. |
Open Chapter 2, Introduction to Linear Polynomials. Each of these eight ideas has its own section.