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Difficulty: 2/102023 NMTC 2023 (QII-68)

Which of these lines is parallel to the line 2y = x+7

Guide / Hint

Hint 1: Find the slope of the line by converting it to (slope is 0.5).

Hint 2: Parallel lines must have the same slope.

Hint 3: Select a line with slope 0.5, such as .

Solution

Step 1 (Find the Slope of the given line): Convert the given equation to slope-intercept form :

So the slope of this line is .

Step 2 (Apply Parallel Line condition): Two lines are parallel if and only if they have the same slope. Therefore, any line parallel to the given line must also have a slope of , such as:

Step 3 (Conclusion): The parallel line is 2y = x (or ).

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    2023 NMTC 2023 QII-68 - Olympiad Math Olympiad Question | Leminno