Answer:
[tex]y=-\dfrac{1}{2}x+2[/tex]
Step-by-step explanation:
Let
x = the amount of time William has been digging
y = the amount he has left to dig
The hole has to be in 2 ft deep. This means when William starts, the hole was 0 feet deep and has left 2 ft to dig. Hence, y-intercept is [tex]b=2[/tex]
He is able to dig at a rate of [tex]\frac{1}{2}[/tex] ft per minute. Thus, the slope is [tex]m=-\frac{1}{2}[/tex] (negative because the depth left to dig is decreasing).
The slope-intercept form of the equation is [tex]y=mx+b,[/tex] so in your case this equation is
[tex]y=-\dfrac{1}{2}x+2[/tex]
