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vlada-n [284]
2 years ago
6

4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant

of variation. Is it direct variation or inverse variation?
Mathematics
1 answer:
Ivan2 years ago
3 0

Question:

The quantities x and y are in proportion

x      y

4      6

30   45

8      b

a      15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

Answer:

a = 10 and b = 12

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

(x_1,y_1) = (4,6)

(x_2,y_2) = (30,45)

The slope (m) is:

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{45 - 6}{30 -4}

m = \frac{39}{26}

m = 1.5

The equation is then calculated using:

y - y_1 = m(x - x_1)

This gives:

y - 6 = 1.5(x - 4)

y - 6 = 1.5x - 6

y = 1.5x

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in y = 1.5x

b = 1.5 * 8

b = 12

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in y = 1.5x

15 = 1.5 * a

Solve for a

a = \frac{15}{1.5}

a = 10

Solving (b): The constant of variation.

This has been solved in (a) above as:

m = 1.5

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

<em>This shows direct variation</em>

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