Question

1. y and x have a proportional relationship, and y = 7 when x = 2. What is the value of x when y = 21?

Answer 1

Answer:

Proportional relationship states that one in which two quantities vary directly with each other.

In other words, we say the variable y varies directly as x if:

  $y = kx$ , where k is constant of proportionality.

(1)

Given: y and x varies a proportional relationship, and y = 7 and x=2

find the value of x when y =21

By the definition of proportional relationship;

y = kx                  ......[1]

Substitute the value y= 7 and x = 2 to solve for k;

$7 = 2k$

Divide by 2 to both sides we get;

$\frac{7}{2} =\frac{2k}{2}$

Simplify:

k = 3.5

Now,  substitute the value of k = 3.5 and y =21 in equation [1] to find the value of x.

$21 = 3.5 x$

Divide both sides by 3.5 we get;

$\frac{21}{3.5} =\frac{3.5x}{3.5}$

Simplify:

x = 6

Therefore, the value of x is 6.

(2)

Given: y and x varies a proportional relationship, and y = 9 and x=2

find the value of y when x=3.

By the definition of proportional relationship;

y = kx                  ......[1]

Substitute the value y= 9 and x = 2 to solve for k;

$9 = k\cdot 2$

Divide by 2 to both sides we get;

$\frac{9}{2} =\frac{2k}{2}$

Simplify:

k = 4.5

Now,  substitute the value of k = 4.5 and x=3 in equation [1] to find the value of y.

$y= 4.5 \cdot 3$

Simplify:

x = 13.5

Therefore, the value of y is 13.5.

(3)

From the given table,

y = 2.8 when x = 2

by the definition of proportional relationship;

$2.8 = k \cdot 2$

or

$2.8 =2k$

Divide by 2 to both sides, we get;

$\frac{2.8}{2} =\frac{2k}{2}$

Simplify:

k = 1.4

Therefore, the equation that represents the table is; y = 1.4 x