Algebra
| English | 中文 | Pinyin |
|---|---|---|
| intercept/ˌɪntəˈsept/ | 截距 | jié jù |
| slope/sləʊp/ | 斜率 | xié lǜ |
A decision before an answer
- A taxi charges a fixed fee and a cost per kilometre. Two journeys let you separate these two charges.
- Your goal: Solve linear equations and inequalities in one variable.
Read the relationship
- Write a variable definition with units before an equation. The intercept represents an initial amount.
- Represent and solve two-variable linear systems.
If 3x+5=20, x is:
Subtract 5 and divide by 3.
Use the defining rule
- A linear slope is change in output divided by change in input. Keep both quantities in the right order.
- Interpret linear functions and parameters in context.
The equations y=2x+1 and y=−x+7 meet at:
2x+1=−x+7 gives x=2, then y=5.
Check the conditions
- Solve systems by substitution or elimination. A solution must satisfy both equations.
- Interpret linear functions and parameters in context.
Let f be the fixed fee and r the cost per kilometre. f+3r=11 and f+7r=19. Subtract the equations: 4r=8, so r=2. Then f=11−3(2)=5. Both journeys fit; the fixed fee is 5.
Solve 4x−3=13. x = ____.
Add 3, then divide 16 by 4.
Apply the task format
- An inequality reverses direction when multiplied or divided by a negative number. Test a value to check the final region.
- Interpret linear functions and parameters in context.
The intercept is not always the actual starting value if zero lies outside the model’s stated domain.
Which answer fits this case?
Solve linear equations and inequalities in one variable
Dividing −2x<6 by −2 gives x<−3.
The sign reverses: x>−3.
Keep the distinctions
- slope 斜率 — Change in output per unit change in input.
- intercept 截距 — The graph’s value when its input is zero.
- Solve linear equations and inequalities in one variable.
- Represent and solve two-variable linear systems.
- Interpret linear functions and parameters in context.
Match each term with its precise meaning in this lesson.
Keep the distinctions stated in the teaching example.
Put this lesson’s reasoning or event sequence in order.
The order follows the stated process; check each stage before the next.