Rainfall and Temperature

📌 CONCEPT: The given scenario can be analyzed using the concept of linear equations in two variables, where the relationship between rainfall and temperature is represented by a straight line. This line can be determined using the given conditions of rainfall rate and temperature range.

📐 RULE / FORMULA: The equation of a straight line can be represented by the formula y = mx + c, where 'm' is the slope of the line, 'x' is the independent variable (temperature in this case), and 'c' is the y-intercept (rainfall when temperature is 0°C).

💡 WORKED EXAMPLE: Given that it rains consistently at a rate of 10 mm/hr when the temperature is between 20°C and 25°C, we can find the equation of the line as follows: Assume the equation to be y = mx + c, where y is the rainfall and x is the temperature. Since the rainfall rate is 10 mm/hr, the slope 'm' can be found as the change in rainfall (10 mm) divided by the change in temperature (5°C) which is 2 mm/°C. Using the given conditions, we can find the y-intercept 'c' as the rainfall when temperature is 0°C, which is 0 mm. The equation of the line becomes y = 2x.

⚠️ COMMON MISTAKE: Students often make mistakes by assuming a non-linear relationship between rainfall and temperature, or by using an incorrect slope value by not considering the given conditions.