Marco graphed the line y=x. He plans to translate the line 5 units up. Which statements are true? Choose more than one answer. CalcAnswer in 5...Select Multiple AnswersAThe translated line will intersect the y-axis at (0, 5).BThe translated line will be parallel to y=x.CThe translated line will intersect the x-axis at (-5, 0).DThe translated line will be perpendicular to y=x.EThe translated line will intersect the y-axis at (0, -5).
Question
Marco graphed the line y=x. He plans to translate the line 5 units up. Which statements are true? Choose more than one answer. CalcAnswer in 5...Select Multiple AnswersAThe translated line will intersect the y-axis at (0, 5).BThe translated line will be parallel to y=x.CThe translated line will intersect the x-axis at (-5, 0).DThe translated line will be perpendicular to y=x.EThe translated line will intersect the y-axis at (0, -5).
Solution
The correct answers are:
A. The translated line will intersect the y-axis at (0, 5). B. The translated line will be parallel to y=x.
Explanation:
A. When a line is translated up or down, the point at which it intersects the y-axis changes. In this case, the line y=x is being translated 5 units up, so the y-intercept will be at (0, 5).
B. Translations do not change the slope of a line. Since the line y=x has a slope of 1, the translated line will also have a slope of 1, meaning it will be parallel to the original line.
C. The translated line will not intersect the x-axis at (-5, 0). Translating a line up or down does not change its x-intercept.
D. The translated line will not be perpendicular to y=x. Translations do not change the slope of a line, so the translated line will not be perpendicular to the original line.
E. The translated line will not intersect the y-axis at (0, -5). The line is being translated up, not down, so the y-intercept will be at (0, 5), not (0, -5).
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