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.
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.