Math  /  Algebra

QuestionSuppose that yy varies directly with xx, and y=9y=9 when x=18x=18. (a) Write a direct variation equation that relates xx and yy.
Equation: \square (b) Find yy when x=5x=5. y=y=\square

Studdy Solution

STEP 1

1. y y varies directly with x x , meaning y=kx y = kx for some constant k k .
2. When x=18 x = 18 , y=9 y = 9 .
3. We need to find the direct variation equation and then calculate y y when x=5 x = 5 .

STEP 2

1. Determine the constant of variation k k .
2. Write the direct variation equation.
3. Use the equation to find y y when x=5 x = 5 .

STEP 3

Since y y varies directly with x x , we have y=kx y = kx .
Given y=9 y = 9 when x=18 x = 18 , substitute these values into the equation to find k k : 9=k×18 9 = k \times 18

STEP 4

Solve for k k : k=918=12 k = \frac{9}{18} = \frac{1}{2}

STEP 5

Substitute the value of k k back into the direct variation equation: y=12x y = \frac{1}{2}x
Equation: y=12x y = \frac{1}{2}x

STEP 6

To find y y when x=5 x = 5 , substitute x=5 x = 5 into the equation: y=12×5=52 y = \frac{1}{2} \times 5 = \frac{5}{2}
The direct variation equation is: y=12x y = \frac{1}{2}x
When x=5 x = 5 , y y is: y=52 y = \frac{5}{2}

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