Answer:
[tex]y=-16x+320[/tex]
144
20 days
Change of the number of skateboards with respect to the change of days.
y intercept represents the total stock of the skateboard wheels.
Step-by-step explanation:
The points on the plane are [tex](3,272)[/tex] and [tex](7,208)[/tex].
Slope is given by
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{208-272}{7-3}\\\Rightarrow m=-16[/tex]
The equation of the line will be
[tex]y-y_1=m(x-x_1)\\\Rightarrow y-272=-16(x-3)\\\Rightarrow y-272=-16x+48\\\Rightarrow y=-16x+320[/tex]
The equation that represents the situation is [tex]y=-16x+320[/tex]
When the number of days is 11 we have [tex]x=11[/tex]
[tex]y=-16\times 11+320\\\Rightarrow y=144[/tex]
The number of wheels left after 11 day is 144.
When the shipment will run out [tex]y=0[/tex]
[tex]0=-16x+320\\\Rightarrow x=\dfrac{320}{16}\\\Rightarrow x=20[/tex]
So, after 20 days the shipment will run out.
The slope represents the change of the number of skateboards with respect to the change of days.
The y intercept represents the total stock of the skateboard wheels.
