Algebra · 代数
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| 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.
答案前的判断
- 出租车收取固定费用及每公里单价。两次行程可帮你分离这两项收费。
- 你的目标：求解单变量线性方程与不等式。
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.
阅读关系
- 在列方程前写出带单位的变量定义。截距代表初始量。
- 表示并求解双变量线性方程组。
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.
运用定义规则
- 线性斜率等于输出变化量除以输入变化量。保持两个量的正确顺序。
- 结合实际情境解释线性函数及其参数。
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.
检查条件
- 通过代入法或消元法解方程组。解必须同时满足两个方程。
- 结合实际情境解释线性函数及其参数。
设 f 为固定费用，r 为每公里单价。f+3r=11 且 f+7r=19。两式相减得：4r=8，故 r=2。然后 f=11−3(2)=5。两次行程均符合；固定费用为 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.
应用题目格式
- 当不等式两边同乘或同除负数时，方向需反转。代入数值检验最终区域是否正确。
- 结合实际情境解释线性函数及其参数。
若零不在模型声明的定义域内，则截距并非实际的起始值。
Which answer fits this case? · 哪个答案符合此案例？
Solve linear equations and inequalities in one variable · 求解一元线性方程与不等式
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.
保持区别
- slope 斜率 — 单位输入变化所引起的输出变化量。
- intercept 截距 — 图像输入为零时的对应值。
- 求解单变量线性方程与不等式。
- 表示并求解双变量线性方程组。
- 结合实际情境解释线性函数及其参数。
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.