Solved on Feb 12, 2024

Describe the linear relationship between $x$ and $y$ . Write the equation $x + 12 = y$ . Find the flower's height after 9 days.

STEP 1

Assumptions
1. The values of $x$ represent the number of days.
2. The values of $y$ represent the height of the flower in centimeters.
3. The relationship between $x$ and $y$ is linear and can be described by an equation.
4. We are given a table with pairs of $x$ and $y$ values.

STEP 2

To describe the relationship in words, observe the table and see how $y$ changes as $x$ changes.

STEP 3

By examining the table, we notice that as $x$ increases, $y$ also increases. Specifically, when $x$ increases by 1, $y$ increases by 1 as well. This suggests a linear relationship with a slope of 1.

STEP 4

To find the specific relationship, we can use any pair of $x$ and $y$ values from the table. For example, when $x = 3$ , $y = 15$ .

STEP 5

Using the pair ( $x = 3$ , $y = 15$ ), we can try to find the equation in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 6

We already observed that the slope $m$ is 1, so we can write the equation as $y = x + b$ .

STEP 7

Substitute $x = 3$ and $y = 15$ into the equation to find $b$ .
$15 = 3 + b$

STEP 8

Solve for $b$ .
$b = 15 - 3$ $b = 12$

STEP 9

Now that we have the slope and the y-intercept, we can write the equation of the relationship.
$y = x + 12$

STEP 10

We can now use this equation to find the flower's height after 9 days. Let $x = 9$ and solve for $y$ .
$y = 9 + 12$

STEP 11

Calculate the value of $y$ .
$y = 21$
The flower's height after 9 days was 21 centimeters.

Was this helpful?

Describe the linear relationship between $x$ and $y$ . Write the equation $x + 12 = y$ . Find the flower's height after 9 days.

STEP 1

Assumptions
1. The values of $x$ represent the number of days.
2. The values of $y$ represent the height of the flower in centimeters.
3. The relationship between $x$ and $y$ is linear and can be described by an equation.
4. We are given a table with pairs of $x$ and $y$ values.

STEP 2

To describe the relationship in words, observe the table and see how $y$ changes as $x$ changes.

STEP 3

By examining the table, we notice that as $x$ increases, $y$ also increases. Specifically, when $x$ increases by 1, $y$ increases by 1 as well. This suggests a linear relationship with a slope of 1.

STEP 4

To find the specific relationship, we can use any pair of $x$ and $y$ values from the table. For example, when $x = 3$ , $y = 15$ .

STEP 5

Using the pair ( $x = 3$ , $y = 15$ ), we can try to find the equation in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 6

We already observed that the slope $m$ is 1, so we can write the equation as $y = x + b$ .

STEP 7

Substitute $x = 3$ and $y = 15$ into the equation to find $b$ .
$15 = 3 + b$

STEP 8

Solve for $b$ .
$b = 15 - 3$ $b = 12$

STEP 9

Now that we have the slope and the y-intercept, we can write the equation of the relationship.
$y = x + 12$

STEP 10

We can now use this equation to find the flower's height after 9 days. Let $x = 9$ and solve for $y$ .
$y = 9 + 12$

STEP 11

Calculate the value of $y$ .
$y = 21$
The flower's height after 9 days was 21 centimeters.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Describe the linear relationship between xxx and yyy. Write the equation x+12=yx + 12 = yx+12=y. Find the flower's height after 9 days.

STEP 1

Assumptions1. The values of xxx represent the number of days.2. The values of yyy represent the height of the flower in centimeters.3. The relationship between xxx and yyy is linear and can be described by an equation.4. We are given a table with pairs of xxx and yyy values.

STEP 2

To describe the relationship in words, observe the table and see how yyy changes as xxx changes.

STEP 3

By examining the table, we notice that as xxx increases, yyy also increases. Specifically, when xxx increases by 1, yyy increases by 1 as well. This suggests a linear relationship with a slope of 1.

STEP 4

To find the specific relationship, we can use any pair of xxx and yyy values from the table. For example, when x=3x = 3x=3, y=15y = 15y=15.

STEP 5

Using the pair (x=3x = 3x=3, y=15y = 15y=15), we can try to find the equation in the form y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 6

We already observed that the slope mmm is 1, so we can write the equation as y=x+by = x + by=x+b.

STEP 7

Substitute x=3x = 3x=3 and y=15y = 15y=15 into the equation to find bbb.15=3+b15 = 3 + b15=3+b

STEP 8

Solve for bbb.b=15−3b = 15 - 3b=15−3 b=12b = 12b=12

STEP 9

Now that we have the slope and the y-intercept, we can write the equation of the relationship.y=x+12y = x + 12y=x+12

STEP 10

We can now use this equation to find the flower's height after 9 days. Let x=9x = 9x=9 and solve for yyy.y=9+12y = 9 + 12y=9+12

STEP 11

Calculate the value of yyy.y=21y = 21y=21The flower's height after 9 days was 21 centimeters.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Describe the linear relationship between $x$ and $y$ . Write the equation $x + 12 = y$ . Find the flower's height after 9 days.

Assumptions
1. The values of $x$ represent the number of days.
2. The values of $y$ represent the height of the flower in centimeters.
3. The relationship between $x$ and $y$ is linear and can be described by an equation.
4. We are given a table with pairs of $x$ and $y$ values.

To describe the relationship in words, observe the table and see how $y$ changes as $x$ changes.

By examining the table, we notice that as $x$ increases, $y$ also increases. Specifically, when $x$ increases by 1, $y$ increases by 1 as well. This suggests a linear relationship with a slope of 1.

To find the specific relationship, we can use any pair of $x$ and $y$ values from the table. For example, when $x = 3$ , $y = 15$ .

Using the pair ( $x = 3$ , $y = 15$ ), we can try to find the equation in the form $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

We already observed that the slope $m$ is 1, so we can write the equation as $y = x + b$ .

Substitute $x = 3$ and $y = 15$ into the equation to find $b$ .
$15 = 3 + b$

Solve for $b$ .
$b = 15 - 3$ $b = 12$

Now that we have the slope and the y-intercept, we can write the equation of the relationship.
$y = x + 12$

We can now use this equation to find the flower's height after 9 days. Let $x = 9$ and solve for $y$ .
$y = 9 + 12$

Calculate the value of $y$ .
$y = 21$
The flower's height after 9 days was 21 centimeters.