Math Snap

STEP 1

Assumptions1. The equation given is $y-32=-3(x-5)$. $y$ represents the amount of water in the pool3. $x$ represents time in hours4. The slope of -3 represents the rate at which the pool is being emptied (3 units per hour)
5. The pool is completely empty when $y=0$

STEP 2

First, we need to rewrite the equation in slope-intercept form ($y=mx+b$), where $m$ is the slope and $b$ is the y-intercept.
$$y-32=-(x-5)$$

STEP 3

istribute the -3 to both terms inside the parentheses.
$$y-32=-3x+15$$

STEP 4

Add32 to both sides of the equation to isolate $y$.
$$y=-3x+15+32$$

STEP 5

implify the equation.
$$y=-3x+47$$

STEP 6

Now that we have the equation in slope-intercept form, we can graph the function. The y-intercept is47 and the slope is -3, which means for every hour that passes, the amount of water in the pool decreases by3 units.

STEP 7

To find out how long it will take to completely empty the pool, we need to find the x-intercept of the graph. The x-intercept is the value of $x$ when $y=0$.
$$0=-3x+47$$

STEP 8

Add $3x$ to both sides of the equation to isolate $x$.
$$3x=47$$

STEP 9

Divide both sides of the equation by3 to solve for $x$.
$$x=47/3$$

Calculate the value of $x$.
$$x=47/3 \approx15.67$$It will take approximately15.67 hours to completely empty the pool.