Studdy AI Logo
Math  /  Algebra

QuestionIf yy varies directly with xx and y=−13y=-13 when x=13x=13, find xx when y=−2y=-2. Write and solve a direct variation equation to find the answer.

Studdy Solution

STEP 1

1. y y varies directly with x x .
2. When x=13 x = 13 , y=−13 y = -13 .
3. We need to find the value of x x when y=−2 y = -2 .

STEP 2

1. Understand the concept of direct variation.
2. Write the direct variation equation.
3. Use the given values to find the constant of variation.
4. Use the constant to find the unknown value of x x .

STEP 3

Understand the concept of direct variation. Direct variation means that y=kx y = kx , where k k is the constant of variation.

STEP 4

Write the direct variation equation using the relationship y=kx y = kx .

STEP 5

Use the given values to find the constant of variation k k . Substitute y=−13 y = -13 and x=13 x = 13 into the equation:
−13=k⋅13 -13 = k \cdot 13
Solve for k k :
k=−1313 k = \frac{-13}{13} k=−1 k = -1

STEP 6

Use the constant k k to find the unknown value of x x when y=−2 y = -2 . Substitute y=−2 y = -2 and k=−1 k = -1 into the equation:
−2=−1⋅x -2 = -1 \cdot x
Solve for x x :
x=−2−1 x = \frac{-2}{-1} x=2 x = 2
The value of x x when y=−2 y = -2 is:
2 \boxed{2}

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord