A line with the equation y=7x−3 is drawn on the coordinate plane. The line is then translated 5 units to the left and 2 units up. Which statement is true?(1 point) Responses The slope of the translated line becomes 7+5, or 12. The slope of the translated line becomes 7+5, or 12. - no response given The slope of the translated line remains 7. The slope of the translated line remains 7. - no response given The slope of the translated line becomes 7+2, or 9. The slope of the translated line becomes 7+2, or 9. - incorrect The slope of the translated line becomes 7–5, or 2.
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When a line is translated (shifted) in the coordinate plane, its slope remains unchanged. The translation affects the position of the line but not its steepness or direction.
In this case, the original line is given by the equation \( y = 7x - 3 \). The slope of this line is 7. After translating the line 5 units to the left and 2 units up, the slope will still be 7.
Therefore, the correct statement is: The slope of the translated line remains 7.
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