Mathematical relationship between two variables that can be expressed by an equation in which one variable is equal to a constant times the other.
y = kx
here k is constant of variation.
The variables x and y vary directly. Write an equation that relates x and y. Then find y when x = 12.
Problem 1 :
x = -18, y = 4
Solution :
The equation is in the form y = kx
4 = k(-18)
4/-18 = k
-2/9 = k
So, the equation that relates x and y is y = -2/9x.
To find y :
y = -2/9x
Substitute the value of x.
y = -2/9(12)
y = -24/9
y = -8/3
y = 2.67
So, the value of y is 2.67 when x = 12.
Problem 2 :
x = 2/3, y = -10
Solution :
The equation is in the form y = kx
-10 = k(2/3)
-10(3/2) = k
-30/2 = k
-15 = k
So, the equation that relates x and y is y = -15x.
To find y :
y = -15x
Substitute the value of x.
y = -15(12)
y = -180
So, the value of y is -180 when x = 12.
The variables x and y vary directly. Write an equation that relates x and y. Then find x when y = -4.
Problem 3 :
x = -12, y = 84
Solution :
The equation is in the form y = kx
84 = k(-12)
84/-12 = k
-7 = k
So, the equation that relates x and y is y = -7x.
To find x :
y = -7x
Substitute the value of y.
-4 = -7x
-4/-7 = x
4/7 = x
0.57 = x
So, the value of x is 0.57 when y = -4.
Problem 4 :
x = -20/3, y = -15/8
Solution :
The equation is in the form y = kx
-15/8 = k(-20/3)
-15/8 × (-3/20) = k
45/160 = k
9/32 = k
So, the equation that relates x and y is y = 9/32x.
To find x :
y = (9/32)x
Substitute the value of y.
-4 = (9/32)x
-4 × (32/9) = x
-128/9 = x
So, the value of x is -128/9 when y = -4.
Problem 5 :
x = -0.5, y = 3.6
Solution :
The equation is in the form y = kx
3.6 = k(-0.5)
(3.6) × (-1/0.5) = k
-3.6/0.5= k
-7.2 = k
So, the equation that relates x and y is y = -7.2x.
To find x :
y = (-7.2)x
Substitute the value of y.
-4 = (-7.2)x
-4 × (-1/7.2) = x
4/7.2 = x
0.56 = x
So, the value of x is 0.56 when y = -4.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM