Solved on Jan 18, 2024

Find the function representing the direct variation between $x$ and $y$ given that $y=14$ when $x=6$ .

STEP 1

Assumptions
1. The value of $y$ varies directly with $x$ , which means $y = kx$ for some constant $k$ .
2. We are given that $y = 14$ when $x = 6$ .
3. We need to find the function that represents the relationship between $x$ and $y$ .

STEP 2

Since $y$ varies directly with $x$ , we can write the relationship as:
$y = kx$

STEP 3

We will use the given point $(x, y) = (6, 14)$ to find the value of the constant $k$ .

STEP 4

Substitute the given values into the direct variation equation.
$14 = k \cdot 6$

STEP 5

Solve for $k$ by dividing both sides of the equation by 6.
$k = \frac{14}{6}$

STEP 6

Simplify the fraction to find the value of $k$ .
$k = \frac{7}{3}$

STEP 7

Now that we have found the constant $k$ , we can write the function that represents the relationship between $x$ and $y$ .
$y = \frac{7}{3}x$
The function that represents the relationship between $x$ and $y$ is $y = \frac{7}{3}x$ .

Was this helpful?

Find the function representing the direct variation between $x$ and $y$ given that $y=14$ when $x=6$ .

STEP 1

Assumptions
1. The value of $y$ varies directly with $x$ , which means $y = kx$ for some constant $k$ .
2. We are given that $y = 14$ when $x = 6$ .
3. We need to find the function that represents the relationship between $x$ and $y$ .

STEP 2

Since $y$ varies directly with $x$ , we can write the relationship as:
$y = kx$

STEP 3

We will use the given point $(x, y) = (6, 14)$ to find the value of the constant $k$ .

STEP 4

Substitute the given values into the direct variation equation.
$14 = k \cdot 6$

STEP 5

Solve for $k$ by dividing both sides of the equation by 6.
$k = \frac{14}{6}$

STEP 6

Simplify the fraction to find the value of $k$ .
$k = \frac{7}{3}$

STEP 7

Now that we have found the constant $k$ , we can write the function that represents the relationship between $x$ and $y$ .
$y = \frac{7}{3}x$
The function that represents the relationship between $x$ and $y$ is $y = \frac{7}{3}x$ .

Start learning now

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

Find the function representing the direct variation between xxx and yyy given that y=14y=14y=14 when x=6x=6x=6.

STEP 1

Assumptions1. The value of y y y varies directly with x x x, which means y=kx y = kx y=kx for some constant k k k.2. We are given that y=14 y = 14 y=14 when x=6 x = 6 x=6.3. We need to find the function that represents the relationship between x x x and y y y.

STEP 2

Since y y y varies directly with x x x, we can write the relationship as:y=kx y = kx y=kx

STEP 3

We will use the given point (x,y)=(6,14)(x, y) = (6, 14)(x,y)=(6,14) to find the value of the constant k k k.

STEP 4

Substitute the given values into the direct variation equation.14=k⋅6 14 = k \cdot 6 14=k⋅6

STEP 5

Solve for k k k by dividing both sides of the equation by 6.k=146 k = \frac{14}{6} k=614​

STEP 6

Simplify the fraction to find the value of k k k.k=73 k = \frac{7}{3} k=37​

STEP 7

Now that we have found the constant k k k, we can write the function that represents the relationship between x x x and y y y.y=73x y = \frac{7}{3}x y=37​xThe function that represents the relationship between x x x and y y y is y=73x y = \frac{7}{3}x y=37​x.

Start learning now

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

Find the function representing the direct variation between $x$ and $y$ given that $y=14$ when $x=6$ .

Assumptions
1. The value of $y$ varies directly with $x$ , which means $y = kx$ for some constant $k$ .
2. We are given that $y = 14$ when $x = 6$ .
3. We need to find the function that represents the relationship between $x$ and $y$ .

Since $y$ varies directly with $x$ , we can write the relationship as:
$y = kx$

We will use the given point $(x, y) = (6, 14)$ to find the value of the constant $k$ .

Substitute the given values into the direct variation equation.
$14 = k \cdot 6$

Solve for $k$ by dividing both sides of the equation by 6.
$k = \frac{14}{6}$

Simplify the fraction to find the value of $k$ .
$k = \frac{7}{3}$

Now that we have found the constant $k$ , we can write the function that represents the relationship between $x$ and $y$ .
$y = \frac{7}{3}x$
The function that represents the relationship between $x$ and $y$ is $y = \frac{7}{3}x$ .