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The graph shows the proportional relationship. Derive the equation of the line y=mx through the origin.Asked by 5
The graph shows the proportional relationship. Derive the equation of the line y = ma through the origin. (1 point)
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GPT-4o mini
In a proportional relationship, the graph of the data is a straight line that passes through the origin (0, 0). The equation of the line can be expressed in the form:
\[ y = mx \]
Where:
- \( y \) represents the dependent variable,
- \( m \) is the constant of proportionality (slope of the line), and
- \( x \) represents the independent variable.
To derive the specific equation \( y = ma \) through the origin, you can simply replace \( m \) with a specific constant if needed. For example, if the slope (constant of proportionality) is represented by \( a \), then the equation can be rewritten as:
\[ y = ax \]
In this case, the relationship indicates that for any value of \( x \), the value of \( y \) is a constant multiple \( a \) of \( x \). Thus, the specific equation that defines the proportional relationship is:
\[ y = ax \]
If a different constant \( m \) needed to be used, you would still follow the same form:
\[ y = mx \]
In summary, the equation of the line based on a proportional relationship through the origin can be expressed as \( y = mx \) or \( y = ax \), depending on how you denote the constant of proportionality.
\[ y = mx \]
Where:
- \( y \) represents the dependent variable,
- \( m \) is the constant of proportionality (slope of the line), and
- \( x \) represents the independent variable.
To derive the specific equation \( y = ma \) through the origin, you can simply replace \( m \) with a specific constant if needed. For example, if the slope (constant of proportionality) is represented by \( a \), then the equation can be rewritten as:
\[ y = ax \]
In this case, the relationship indicates that for any value of \( x \), the value of \( y \) is a constant multiple \( a \) of \( x \). Thus, the specific equation that defines the proportional relationship is:
\[ y = ax \]
If a different constant \( m \) needed to be used, you would still follow the same form:
\[ y = mx \]
In summary, the equation of the line based on a proportional relationship through the origin can be expressed as \( y = mx \) or \( y = ax \), depending on how you denote the constant of proportionality.
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