To write the equations of the solid line and the dotted line in your system of linear equations, we need to analyze the slope and intercepts based on the description you provided.
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Solid Line: You mentioned that the solid line intersects the y-axis at (0, 3). This gives us the y-intercept (b) for this line. Since the line is sloping upward and is parallel to another line (the dotted line), its slope (m) will be positive. Without additional information about the slope, we can express it generally.
Thus, the equation for the solid line can be written as: \[ y = mx + 3 \] where \(m\) is the slope.
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Dotted Line: The dotted line passes through the point (0, 0) which means the y-intercept is 0. Since you mentioned the lines are parallel, the dotted line would have the same slope as the solid line (let's also call it \(m\)). Therefore, the equation for the dotted line becomes: \[ y = mx \]
So, the equations of the system of linear equations graphed are:
- The equation of the solid line is \(y = mx + 3\).
- The equation of the dotted line is \(y = mx\).
If you need a specific numeric slope or more details to finalize these equations, please provide additional information.
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