Let x represents the time and y represents the temperature.
Now let x=0 is corresponds to 12 AM. Thus, 5 AM is corresponds to x=5. And we have been given that temperature at a ski resort was 12°F at 5:00 A.M. Thus, we have a point (5,12)
Now, the rate is given by [tex]m=1.5[/tex]
Using the point slope form of a line, the equation of line is given by
[tex]y-y_1=m(x-x_1)\\
y-12=1.5(x-5)\\
y-12=1.5x-7.5\\
y=1.5x+4.5[/tex]
Now, we have to find the value for y for x=12
On substituting the value of x in the above equation, we get
[tex]y=1.5\times 12+4.5\\
\\
y=22.5[/tex]
Therefore, the temperature at 12 noon is 22.5°F
