Question

what is the equation of the graph below? (4 pts) equation: ______ graph the equation y = -2x + 1 (3 pts) in antelope, ca it is currently 70 degrees. the temperature is rising 2 degrees per hour. in death valley it is currently 80 degrees and is rising 15 degrees per hour. a. write an equation to represent each city. (2 pts) antelope: death valley: b. what does the slope represent for the city of antelope? (1 pt) c. what does the y - intercept represent for the city of death valley? (1 pt) d. what will the temperature be in each city after 5 hours? (2 pts) antelope: death valley: e. it is unlikely that a human will survive when the temperature is 122 degrees or hotter. look back at your answer from problem d. would a human survive in both cities? explain. (2 pts)

Explanation:

Step1: Find equations for temperature in each city

The general form of a linear - equation is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value). For Antelope, the initial temperature ($b$) is 70 degrees and the rate of change ($m$) is 2 degrees per hour. So the equation is $y = 2x+70$. For Death Valley, the initial temperature ($b$) is 80 degrees and the rate of change ($m$) is 15 degrees per hour. So the equation is $y = 15x + 80$.

Step2: Interpret the slope for Antelope

The slope of the equation for Antelope ($y = 2x+70$) is 2. The slope represents the rate at which the temperature is changing. So, it represents the increase in temperature per hour, which is 2 degrees per hour.

Step3: Interpret the y - intercept for Death Valley

The y - intercept of the equation for Death Valley ($y = 15x + 80$) is 80. The y - intercept represents the initial value of the function. So, it represents the current temperature in Death Valley, which is 80 degrees.

Step4: Calculate temperatures after 5 hours

For Antelope, substitute $x = 5$ into $y = 2x+70$. So, $y=2\times5 + 70=10 + 70=80$ degrees. For Death Valley, substitute $x = 5$ into $y = 15x + 80$. So, $y=15\times5+80 = 75+80=155$ degrees.

Step5: Determine human survival

In Antelope, the temperature after 5 hours is 80 degrees, which is less than 122 degrees. So a human can survive. In Death Valley, the temperature after 5 hours is 155 degrees, which is greater than 122 degrees. So a human cannot survive.

Answer:

a. Antelope: $y = 2x+70$, Death Valley: $y = 15x + 80$
b. The increase in temperature per hour (2 degrees per hour)
c. The current temperature in Death Valley (80 degrees)
d. Antelope: 80 degrees, Death Valley: 155 degrees
e. A human can survive in Antelope but not in Death Valley. In Antelope, the temperature after 5 hours is 80 degrees ($<122$ degrees), while in Death Valley, the temperature after 5 hours is 155 degrees ($>122$ degrees).