QuestionGraph the equation $y-32=-3(x-5)$ to find how long it takes to empty the pool.

Studdy Solution

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 $x$ .
$x=47/3$

STEP 10

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

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QuestionGraph the equation $y-32=-3(x-5)$ to find how long it takes to empty the pool.

Studdy Solution

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 $x$ .
$x=47/3$

STEP 10

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

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QuestionGraph the equation y−32=−3(x−5)y-32=-3(x-5)y−32=−3(x−5) to find how long it takes to empty the pool.

Studdy Solution

STEP 1

STEP 2

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

STEP 3

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

STEP 4

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

STEP 5

implify the equation.y=−3x+47y=-3x+47y=−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 xxx when y=0y=0y=0.0=−3x+470=-3x+470=−3x+47

STEP 8

Add 3x3x3x to both sides of the equation to isolate xxx.3x=473x=473x=47

STEP 9

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

STEP 10

Calculate the value of xxx.x=47/3≈15.67x=47/3 \approx15.67x=47/3≈15.67It will take approximately15.67 hours to completely empty the pool.

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QuestionGraph the equation $y-32=-3(x-5)$ to find how long it takes to empty the pool.

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.
$y-32=-(x-5)$

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

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

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

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 $y=0$ .
$0=-3x+47$

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

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.