Question

when emmy went to bed, it was a frigid 9°f outside. the temperature has been dropping 2°f each hour. write an equation that shows the relationship between the number of hours since emmy went to bed, x, and the temperature in °f, y. y =

Explanation:

Step1: Identify initial temperature and rate of change

The initial temperature (when \( x = 0 \), i.e., when Emmy just went to bed) is \( 9^\circ\text{F} \). The temperature drops \( 2^\circ\text{F} \) each hour, so the rate of change (slope) is \( -2 \) (negative because the temperature is decreasing).

Step2: Use slope - intercept form of a linear equation

The slope - intercept form of a linear equation is \( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept (initial value). Here, \( m=- 2 \) (the rate of temperature drop per hour) and \( b = 9 \) (the initial temperature). Substituting these values into the equation, we get \( y=-2x + 9 \).

Answer:

\( y=-2x + 9 \)