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How to Write a Proportional Relationship Equation for the Table with x=4,5,6 and y=6,15/2,9
Mathematics
Grade 7
Question Content
Write an equation that models the proportional relationship shown in the table: \n| x | y |\n|---|---|\n| 4 | 6 |\n| 5 | 15/2 |\n| 6 | 9 |
Correct Answer
y = (3/2)x or y = 1.5x
Detailed Solution Steps
1
Step 1: Remember that proportional relationships use the standard form y = kx, where k is the constant of proportionality.
2
Step 2: Calculate k using the first pair (4, 6): k = y/x = 6/4 = 3/2 (or 1.5 as a decimal).
3
Step 3: Verify k with the other pairs: For (5, 15/2), k = (15/2)/5 = 15/10 = 3/2; For (6, 9), k = 9/6 = 3/2. The constant is consistent across all pairs.
4
Step 4: Substitute k = 3/2 into the proportional equation form to get y = (3/2)x.
Knowledge Points Involved
1
Proportional Relationship Equation
A proportional relationship between two variables x and y is defined by the linear equation y = kx, where k is a non-zero constant called the constant of proportionality. This means y is always a constant multiple of x, and the graph of the relationship is a straight line passing through the origin (0,0).
2
Constant of Proportionality with Fractions
When working with fractional y-values, the constant of proportionality k is still calculated as y/x. Simplify the resulting fraction to its lowest terms to get the exact value of k for the proportional equation.
3
Verification of Proportional Relationships
To confirm a relationship is proportional, check that the ratio y/x is the same for all pairs of (x,y) values in the dataset. If all ratios are equal, the relationship is proportional; if not, it is non-proportional.
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