To analyze the situation with lines B and C, let's start by defining what we have:
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Line B: This line crosses at the origin (0,0). Since it's a straight line with a y-intercept of 0, we can express Line B's equation as: \[ y = mx \] where \( m \) is the slope of the line.
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Line C: This line is parallel to Line B but shifted downwards. Since it crosses the y-axis at (0, -5), we can express its equation as: \[ y = mx - 5 \]
Now let's discuss the operations you've mentioned:
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Moved down 5 units: This operation suggests that we are further translating Line C downwards. The new y-intercept of Line C after translating down 5 units would be: \[ -5 - 5 = -10 \] Therefore, the equation for the new Line C (let's call it Line C') would be: \[ y = mx - 10 \]
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Decreased by factor of 5: This operation implies that we are scaling the line vertically by a factor of \( \frac{1}{5} \). To scale Line C' by a factor of \( \frac{1}{5} \), we can multiply the entire equation of Line C' by \( \frac{1}{5} \): \[ y = \frac{1}{5}(mx - 10) \] This simplifies to: \[ y = \frac{m}{5}x - 2 \]
In summary, after moving Line C down by 5 units and then scaling it by a factor of 5, the new equation of Line C becomes: \[ y = \frac{m}{5}x - 2 \]
If you need anything else, such as specific values for \( m \) or any additional properties of these lines, please let me know!