Class 8 Exam > Class 8 Questions > In the context of direct variation, which sta... Start Learning for Free
In the context of direct variation, which statement is accurate?
- a)The quantities are unrelated.
- b)The relationship is quadratic.
- c)The relationship is exponential.
- d)The relationship is linear, and the graph is a straight line.
Correct answer is option 'D'. Can you explain this answer?
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In the context of direct variation, which statement is accurate?a) The...
Understanding Direct Variation
Direct variation describes a specific relationship between two variables, typically denoted as x and y. When we say y varies directly with x, it means that as one quantity increases, the other does too, in a consistent manner.
Key Characteristics of Direct Variation:
- Linear Relationship: In direct variation, the relationship between the two variables is linear. This means that if you plot the values on a graph, they will form a straight line.
- Equation Form: The relationship can be expressed in the form y = kx, where k is a constant. This constant indicates how much y changes for each unit change in x.
- Proportionality: The variables are proportional to each other. If x doubles, y also doubles, maintaining the same ratio throughout.
Visual Representation:
- Graphing: When you graph the equation y = kx, the line will pass through the origin (0,0) and have a slope equal to the constant k.
- Example: If k = 2, then for every unit increase in x, y increases by 2 units. For instance, if x = 1, y = 2; if x = 2, y = 4, illustrating a straight line.
Conclusion:
Thus, the correct statement regarding direct variation is option D: “The relationship is linear, and the graph is a straight line.” This fundamental concept is crucial for understanding relationships in mathematics and is widely applicable in real-world scenarios.
Direct variation describes a specific relationship between two variables, typically denoted as x and y. When we say y varies directly with x, it means that as one quantity increases, the other does too, in a consistent manner.
Key Characteristics of Direct Variation:
- Linear Relationship: In direct variation, the relationship between the two variables is linear. This means that if you plot the values on a graph, they will form a straight line.
- Equation Form: The relationship can be expressed in the form y = kx, where k is a constant. This constant indicates how much y changes for each unit change in x.
- Proportionality: The variables are proportional to each other. If x doubles, y also doubles, maintaining the same ratio throughout.
Visual Representation:
- Graphing: When you graph the equation y = kx, the line will pass through the origin (0,0) and have a slope equal to the constant k.
- Example: If k = 2, then for every unit increase in x, y increases by 2 units. For instance, if x = 1, y = 2; if x = 2, y = 4, illustrating a straight line.
Conclusion:
Thus, the correct statement regarding direct variation is option D: “The relationship is linear, and the graph is a straight line.” This fundamental concept is crucial for understanding relationships in mathematics and is widely applicable in real-world scenarios.
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In the context of direct variation, which statement is accurate?a) The...
In direct variation, the relationship between the two quantities is linear, represented graphically by a straight line passing through the origin.
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