AQA A Level Maths: Pure复习笔记2.7.4 Proportional Relationships
Proportional Relationships
Proportional relationships
- Proportional relationships describe a proportional connection between two variables
- This can happen in two ways
- Direct proportion
- one variable increases or decreases the other does the same
- Inverse proportion
- one variable increases the other decreases and vice versa
- Direct proportion
- Proportional relationships use the symbol ∝ which means is proportional to
- Both direct and inverse proportion can be represented graphically
- Direct proportion creates a linear graph where k is the gradient
- Inverse proportion creates a reciprocal graph
Direct proportion
- Υ∝Χ means y is proportional to x
- y increases as x does, k determines the rate (gradient)
- by changing this to the equation Υ = kΧ we can substitute in given values and solve to find k
- Note that this means the ratio of x and y is constant k = y / x
Inverse proportion
How do I work with proportional relationships?
-
- Set up your proportional relationship using then change to = k
- Be clear about what y is proportional to …
- “… the square of x” (x2)
- “… x plus four” (x + 4)
- Calculate or deduce the value of k from the information given or a graph
- Once you've found k sub it back in to your original proportion equation
- You can now find any values using this proportional relationship
- y = mx + c rearranges to y – c = mx so (y - c) is directly proportional to x
- Proportional relationships are often used in modelling
Worked Example
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