QuestionA direct variation includes the points $\left(-\frac{3}{2}, \frac{9}{4}\right)$ and $\left(-\frac{6}{5}, n\right)$ . Find $n$ . Write and solve a direct variation equation to find the answer. Simplify any fractions. $n=$ $\square$ Submit

Studdy Solution

STEP 1

1. The relationship between the variables is a direct variation.
2. The direct variation equation is in the form $y = kx$ , where $k$ is the constant of variation.
3. We have two points: $\left(-\frac{3}{2}, \frac{9}{4}\right)$ and $\left(-\frac{6}{5}, n\right)$ .
4. We need to find the value of $n$ .

STEP 2

1. Determine the constant of variation $k$ using the first point.
2. Use the constant $k$ to find $n$ using the second point.

STEP 3

Determine the constant of variation $k$ using the first point $\left(-\frac{3}{2}, \frac{9}{4}\right)$ .
The direct variation equation is $y = kx$ .
Substitute the values from the first point into the equation:
$\frac{9}{4} = k \left(-\frac{3}{2}\right)$
Solve for $k$ :
$k = \frac{9}{4} \div \left(-\frac{3}{2}\right)$
$k = \frac{9}{4} \times \left(-\frac{2}{3}\right)$
$k = -\frac{9 \times 2}{4 \times 3}$
$k = -\frac{18}{12}$
Simplify the fraction:
$k = -\frac{3}{2}$

STEP 4

Use the constant $k = -\frac{3}{2}$ to find $n$ using the second point $\left(-\frac{6}{5}, n\right)$ .
Substitute $k$ and the $x$ -value of the second point into the direct variation equation:
$n = k \left(-\frac{6}{5}\right)$
$n = -\frac{3}{2} \times \left(-\frac{6}{5}\right)$
$n = \frac{3 \times 6}{2 \times 5}$
$n = \frac{18}{10}$
Simplify the fraction:
$n = \frac{9}{5}$
The value of $n$ is:
$n = \boxed{\frac{9}{5}}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

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

Parents Influencer program Contact Policy Terms