b.
Use rise over run to find the slope. Rise over run uses the following formula:
[tex] \frac{y_{2}-y_{1}}{x_{2}-x_{1}} [/tex]
We have two known points in the graph: (0,0) and (10, -35). Plug the values into the equation:
[tex]y_{1} = 0, y_{2} = 35, x_{1} = 0, x_{2} = 10[/tex]
[tex] \frac{-35 - 0}{10 - 0} = \frac{-35}{10} = -3.5[/tex]
The slope of the graph is -3.5. Including units, this would be -3.5 degrees per thousand feet.
c.
The question includes a starting point for the temperature and the change in thousands of feet. Since the change is 5500, we'll divide this by 1000 to get the x-value:
[tex]5500 \div 1000 = 5.5[/tex]
[tex]x = 5.5[/tex]
The starting temperature will be our y-int for our slope intercept equation:
[tex]b = 74[/tex]
[tex]y = -3.5x + 74[/tex]
Plug in your x value:
[tex]-3.5(5.5) + 74 = -19.25 + 74 = 55.75[/tex]
The temperature at the top of the mountain is 55.75 degrees.
