Question
The temperature is 17 degrees Fahrenheit at 8:00 p.m. It is expected to drop 2.5 degrees as each hour passes. Write the linear equation that represents this scenario and explain what the y-intercept represents.
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Answered by
GPT 3.5
To write the linear equation that represents this scenario, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, we are told that the temperature is expected to drop 2.5 degrees as each hour passes. This means that the slope of the linear equation is -2.5, because the temperature is decreasing.
So, the linear equation representing this scenario is:
y = -2.5x + b
To find the y-intercept, we can use the initial temperature provided at 8:00 p.m., which is 17 degrees Fahrenheit. Plugging this into the equation, we get:
17 = -2.5(0) + b
17 = b
Therefore, the y-intercept of the linear equation is 17. This means that at x = 0 (which represents 8:00 p.m.), the temperature is 17 degrees Fahrenheit. The y-intercept represents the initial temperature at the starting point of the scenario.
In this case, we are told that the temperature is expected to drop 2.5 degrees as each hour passes. This means that the slope of the linear equation is -2.5, because the temperature is decreasing.
So, the linear equation representing this scenario is:
y = -2.5x + b
To find the y-intercept, we can use the initial temperature provided at 8:00 p.m., which is 17 degrees Fahrenheit. Plugging this into the equation, we get:
17 = -2.5(0) + b
17 = b
Therefore, the y-intercept of the linear equation is 17. This means that at x = 0 (which represents 8:00 p.m.), the temperature is 17 degrees Fahrenheit. The y-intercept represents the initial temperature at the starting point of the scenario.
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