1. a.
- Graph: Plotting the points (0,0), (1,3), (2,6), (3,9), (4,12) results in a straight line passing through the origin, indicating direct proportionality.
- Constant of proportionality: k = y/x = 3/1 = 3. Equation: y = 3x.
- Missing value: When x = 10, y = 3 * 10 = 30.
b.
- Graph: Plotting the points (0,0), (2.5,10), (5,20), (7.5,30), (10,40) results in a straight line passing through the origin, indicating direct proportionality.
- Constant of proportionality: k = y/x = 10/2.5 = 4. Equation: y = 4x.
- Missing value: When y = 100, x = 100 / 4 = 25.
c.
- Graph: Plotting the points (-0.2,-0.1), (-0.1,-0.05), (0,0), (0.4,0.2), (0.8,0.4) results in a straight line passing through the origin, indicating direct proportionality.
- Constant of proportionality: k = y/x = 0.2/0.4 = 0.5. Equation: y = 0.5x.
- Missing value: When x = 10, y = 0.5 * 10 = 5.
d.
- Graph: Plotting the points (-4,-4.8), (-2,-2.4), (5,6), (10,12), (12,14.4) results in a straight line passing through the origin, indicating direct proportionality.
- Constant of proportionality: k = y/x = 6/5 = 1.2. Equation: y = 1.2x.
- Missing value: When y = 0.6, x = 0.6 / 1.2 = 0.5.
2.
- Constant of proportionality: k = y/x = 15 / 0.15 = 100.
- Equation: y = 100x.
3. a.
- Inverse proportionality check: xy = 1*1 = 1, 2*0.5 = 1, 3*0.333... ≈ 1, 4*0.25 = 1. The product xy is constant (k=1), so they are inversely proportional.
- Constant of proportionality: k = 1. Equation: y = 1/x.
- Missing value: When y = 2, x = 1 / 2 = 0.5.
b.
- Inverse proportionality check: xy = 1*50 = 50, 2*25 = 50, 4*12.5 = 50, 10*5 = 50. The product xy is constant (k=50), so they are inversely proportional.
- Constant of proportionality: k = 50. Equation: y = 50/x.
- Missing value: When x = 20, y = 50 / 20 = 2.5.
c.
- Inverse proportionality check: xy = 0.2*4 = 0.8, 0.4*2 = 0.8, 2*0.4 = 0.8, 8*0.1 = 0.8. The product xy is constant (k=0.8), so they are inversely proportional.
- Constant of proportionality: k = 0.8. Equation: y = 0.8/x.
- Missing value: When x = -0.1, y = 0.8 / (-0.1) = -8.
d.
- Inverse proportionality check: xy = (-2)*(-30) = 60, (-3)*(-20) = 60, (-5)*(-12) = 60, (-12)*(-5) = 60. The product xy is constant (k=60), so they are inversely proportional.
- Constant of proportionality: k = 60. Equation: y = 60/x.
- Missing value: When x = 90, y = 60 / 90 = 2/3.
4.
- Constant of proportionality: k = xy = 3 * 4.5 = 13.5.
- Equation: y = 13.5/x.
- When y = 2, x = 13.5 / 2 = 6.75.
Parent Tip: Review the logic above to help your child master the concept of direct proportion worksheet.
