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.
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 ).
A linear relationship will show up on a graph as a straight line.
An equation represents the relationship between variables by expressing how one quantity depends on others through mathematical relationships. For example, in the equation (y = mx + b), (y) is dependent on the variable (x), with (m) representing the slope and (b) the y-intercept. This relationship allows us to predict the value of (y) based on different values of (x), illustrating how changes in one variable affect another. Thus, equations serve as a concise way to model and analyze relationships in various situations.
Line graph is used to show relationship between two variables.
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.
Inversely proportional
inversely proportional
inversely proportional
inversely proportional
Inversely proportional
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 ).
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.
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The answer requires the relevant context to be given.
pyramid
You can use a plot diagram to plot the points and if they all go straight through the origin then it is proportional