9)
If y varies directly with x and y = -3 when x = 6, find y when x = 14.
We know if y varies directly with x, we get the equation
y ∝ x
y = kx
k = y/x
where k is called the constant of variation.
we are given y = -3 when x = 6
so substitute y = -3 and x = 6 to determine 'k'
k = y/x
k = -3/6 = -1/2
Now we have to find y when x = 14
so substituting x = 14 and k = -1/2 to find y
y = kx
y = -1/2 × 14 = -7
Therefore, the value of y = -7 when x = 14
10) If y is directly proportional to x and y = 4 when x = 3, find x when y = -12.
we are given y = 4 when x = 3
so substitute y = 4 and x = 3 to determine 'k'
k = y/x
k = 4/3
Now we have to find x when y = -12
so substituting y = -12 and k = 4/3 to find x
y = kx
x = y/k
x = [-12] / [4/3] = [-12×3] / [4]
x = -36/4
x = -9
Therefore, the value of x = -9 when x = 3
11)
If y varies directly with x and y = -6 when x = 2, find the constant of variation.
We are given
y = -6
x = 2
so substitute y = -6 and x = 2 in the equation
k = y/x
k = -6/2
k = -3
Therefore, the value of the constant of variation will be:
