Question

William is digging a hole to plant a tree.The hole has to be in 2 ft deep.He is able to dig at a rate of 1/2 ft. per minute.Write an equation for when y,the amount he has left to dig is a function of x,the amount of time he has been digging

Answer 1

Answer:

$y=-\dfrac{1}{2}x+2$

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 $b=2$

He is able to dig at a rate of $\frac{1}{2}$ ft per minute. Thus, the slope is $m=-\frac{1}{2}$ (negative because the depth left to dig is decreasing).

The slope-intercept form of the equation is $y=mx+b,$ so in your case this equation is

$y=-\dfrac{1}{2}x+2$