Find one variable value given the other and interpret in context.
Substitute the known value, solve, and interpret the result in context.
核心知识
Substitute a known value for one variable, solve for the other, then connect the answer to what the variables represent in the problem's real-world context.
深入理解
Many SAT questions give a linear equation modeling a situation — total cost, remaining distance, temperature conversion — and ask you to find one quantity when the other is known. The algebra is straightforward substitution. The harder part is interpreting the result.
When a question says "what does the value 25 represent in this equation," it's asking about context, not computation. The slope represents the rate of change per unit, and the y-intercept represents the initial or fixed value. For example, in
Always label your answer with units or meaning. The SAT often includes distractors that are numerically correct but attached to the wrong interpretation.
分步讲解
- Identify which variable is known and substitute its value into the equation.
- Solve for the remaining variable using inverse operations.
- Interpret the result: what does this variable represent in context?
- Check that units and meaning match the question being asked.
常见误解
- Solving correctly but choosing a distractor that misinterprets the variable — e.g., giving the number of items when the question asks for cost.
- Confusing slope with y-intercept in context: the slope is the per-unit rate, not the starting value.
- Plugging into the wrong variable — read carefully whether the given value is x or y in the model.
示例解析
A plumber charges a flat fee plus an hourly rate. The total cost in dollars is modeled by
选择一个答案查看解析