Answer:
(a) We will form an equation of line from the points given (6,10) and (2,15)
Using:[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}\cdot (x-x_1)[/tex]
On substituting the values in the formula above we will get the required equation of line.
[tex]y-10=\frac{15-10}{2-6}\cdot (x-6)[/tex]
[tex]\Rightarrow y-10=\frac{5}{-4}\cdot (x-6)[/tex]
On simplification we will get:
[tex]y=\frac{1}{4}(-5x+70)[/tex]
(b) We need to tell at day 0 put x=0 in above equation:
[tex]y=\frac{1}{4}(-5\cdot 0+70)[/tex]
[tex]y=70[/tex]
Anika worked for 70 hours on the set up crew on the day the fair arrived at the fairgrounds day 0.
Now, we need to tell decrease per day which is equal to the slope of line
To find the slope compare the equation with general equation which is y=mx+c where m is slope
Here, in [tex]y=\frac{1}{4}(-5x+70)[/tex]
[tex]m=\frac{-5}{4}[/tex] which is the decrease per day.
