🧱 See It
Suppose you start with $3 and save $2 every week. After week 1 you have $5, after week 2 you have $7, and so on. There's a rule connecting "which week" to "how much saved," and it works the exact same way every single week.
| Week | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| Total Saved ($) | 5 | 7 | 9 | 11 |
Each week adds exactly $2 — the same jump every time. That steady jump is what makes it linear.
✏️ Draw It
Plot "week" along the bottom and "total saved" up the side. Each week is one dot — there's no dot for "week 2.5" because that doesn't mean anything here, which is why this is called a discrete relation:
The dots line up in a perfectly straight path — that's what makes this a linear relation. The dashed line is just a guide for your eye; only the dots themselves are real data.
🔢 Write It
Using x for the week number and y for the total saved, the rule becomes an equation:
y = 2x + 3
Check it against week 3: y = 2(3) + 3 = 9 — matches the table.
💡 Worked Examples
Example 1 — Use the rule: y = 3x − 1, find y when x = 4
- Substitute:
y = 3(4) − 1 - Multiply:
y = 12 − 1 - Answer:
y = 11
Example 2 — Does this table fit y = 2x + 1?
| x | 1 | 2 | 3 |
|---|---|---|---|
| y | 3 | 5 | 7 |
- Check x=1:
2(1)+1 = 3— matches. - Check x=2:
2(2)+1 = 5— matches. - Check x=3:
2(3)+1 = 7— matches. - Answer: Yes, every pair fits the rule.
🧠 Quick Reference
y = ___x + ___.