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How does a graph show a proportional relationship?
A graph shows a proportional relationship when it displays a straight line that passes through the origin (0,0). This indicates that as one variable increases or decreases, the other variable does so at a constant rate. The slope of the line represents the constant ratio between the two variables, confirming their proportionality. If the line is not straight or does not pass through the origin, the relationship is not proportional.
How do you find proportional relationships?
To find proportional relationships, you can compare the ratios of two quantities to see if they remain constant. This can be done by setting up a ratio (e.g., ( \frac{y_1}{x_1} = \frac{y_2}{x_2} )) for different pairs of values. If the ratios are equal, the relationship is proportional. Additionally, graphing the values will show a straight line through the origin if the relationship is proportional.
Which graph best represents the following situation As x increases y increases?
The graph that best represents the situation where "as x increases, y increases" is a positively sloped line or curve. This means that the graph should show a consistent upward trend, indicating that for every increase in the value of x, there is a corresponding increase in the value of y. Linear or exponential growth patterns are both suitable representations of this relationship.
Does the equation y13x show a proportional relationship between x and y?
The equation ( y = 13x ) does represent a proportional relationship between ( x ) and ( y ). In this equation, ( y ) is directly proportional to ( x ) with a constant of proportionality equal to 13. This means that if ( x ) increases or decreases, ( y ) will change by the same factor, maintaining a constant ratio of ( \frac{y}{x} = 13 ).
Which equation can be used to show the relationship between the circumference C and the diameter d of a circle?
The relationship between the circumference ( C ) and the diameter ( d ) of a circle is expressed by the equation ( C = \pi d ), where ( \pi ) (approximately 3.14159) is a constant that represents the ratio of the circumference to the diameter of any circle. This equation indicates that the circumference is directly proportional to the diameter, with ( \pi ) as the proportionality constant.
How does a graph show a proportional relationship?
A graph shows a proportional relationship when it displays a straight line that passes through the origin (0,0). This indicates that as one variable increases or decreases, the other variable does so at a constant rate. The slope of the line represents the constant ratio between the two variables, confirming their proportionality. If the line is not straight or does not pass through the origin, the relationship is not proportional.
What type of relationship does increased distance and gravity show?
Inversely proportional
What relationship does increased distance and decreased gravity show?
inversely proportional
What type relationship does increased distance and decrease gravity show?
inversely proportional
What type of relationship does increased distance and deceased gravity show?
inversely proportional
What type of relationship does increased distance and decrease gravity show?
Inversely proportional
How do you find proportional relationships?
To find proportional relationships, you can compare the ratios of two quantities to see if they remain constant. This can be done by setting up a ratio (e.g., ( \frac{y_1}{x_1} = \frac{y_2}{x_2} )) for different pairs of values. If the ratios are equal, the relationship is proportional. Additionally, graphing the values will show a straight line through the origin if the relationship is proportional.
Which graph best represents the following situation As x increases y increases?
The graph that best represents the situation where "as x increases, y increases" is a positively sloped line or curve. This means that the graph should show a consistent upward trend, indicating that for every increase in the value of x, there is a corresponding increase in the value of y. Linear or exponential growth patterns are both suitable representations of this relationship.
Does the equation y13x show a proportional relationship between x and y?
The equation ( y = 13x ) does represent a proportional relationship between ( x ) and ( y ). In this equation, ( y ) is directly proportional to ( x ) with a constant of proportionality equal to 13. This means that if ( x ) increases or decreases, ( y ) will change by the same factor, maintaining a constant ratio of ( \frac{y}{x} = 13 ).
Which equation can be used to show the relationship between the circumference C and the diameter d of a circle?
The relationship between the circumference ( C ) and the diameter ( d ) of a circle is expressed by the equation ( C = \pi d ), where ( \pi ) (approximately 3.14159) is a constant that represents the ratio of the circumference to the diameter of any circle. This equation indicates that the circumference is directly proportional to the diameter, with ( \pi ) as the proportionality constant.
How can you use a table to determine if there is a proportional relationship between two quantities?
To determine if there is a proportional relationship between two quantities using a table, you can check if the ratio of the two quantities remains constant across all entries. Specifically, divide each value of one quantity by the corresponding value of the other quantity for each row; if all ratios are the same, the relationship is proportional. Additionally, the table should show that when one quantity is multiplied by a constant, the other quantity increases by the same factor. If these conditions are met, the two quantities are proportional.
Describe in your own words a graph of charles law?
A graph of Charles's Law would show a direct relationship between the volume of a gas and its temperature at constant pressure. As temperature increases, the volume of the gas also increases proportionally. This relationship is represented by a straight line passing through the origin on a graph where the x-axis represents temperature and the y-axis represents volume.
