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Find the constant of proportionality k. Then write an equation for the relationship between x and y

User Bonna
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Question:

Find the constant of proportionality k. Then write an equation for the relationship between x and y


\begin{array}{ccccc}x & {2} & {4} & {6} & {8} \ \\ y & {10} & {20} & {30} & {40} \ \ \end{array}

Answer:

(a)
k = 5

(b)
y = 5x

Explanation:

Given


\begin{array}{ccccc}x & {2} & {4} & {6} & {8} \ \\ y & {10} & {20} & {30} & {40} \ \ \end{array}

Solving (a): The constant of proportionality:

Pick any two corresponding x and y values


(x_1,y_1) = (2,10)


(x_2,y_2) = (6,30)

The constant of proportionality k is:


k = (y_2 - y_1)/(x_2 - x_1)


k = (30-10)/(6-2)


k = (20)/(4)


k = 5

Solving (b): The equation

In (a), we have:


(x_1,y_1) = (2,10)

k can also be expressed as:


k = (y- y_1)/(x- x_1)

Substitute values for x1, y1 and k


5 = (y- 10)/(x- 2)

Cross multiply:


y - 10 = 5(x - 2)

Open bracket


y - 10 = 5x - 10

Add 10 to both sides


y - 10 +10= 5x - 10+10


y = 5x

User Raanan Avidor
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