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How to Write a Proportional Relationship Equation for the Table with x=3,5,7 and y=-12,-20,-28
Mathematics
Grade 7
Question Content
Write an equation that models the proportional relationship shown in the table: \n| x | y |\n|---|---|\n| 3 | -12 |\n| 5 | -20 |\n| 7 | -28 |
Correct Answer
y = -4x
Detailed Solution Steps
1
Step 1: Recall that a proportional relationship follows the form y = kx, where k is the constant of proportionality (unit rate).
2
Step 2: Calculate k using any pair of x and y values from the table. Use the first pair (3, -12): k = y/x = -12/3 = -4.
3
Step 3: Verify k with the other pairs: For (5, -20), k = -20/5 = -4; For (7, -28), k = -28/7 = -4. The constant is consistent.
4
Step 4: Substitute k = -4 into the proportional equation form to get y = -4x.
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
The constant of proportionality k is calculated as the ratio of y to x (k = y/x) for any corresponding pair of values in a proportional relationship. It represents the unit rate of change of y with respect to x.
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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