What is the equation of the line parallel to y = 3x - 2 that passes through the

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Question: What is the equation of the line parallel to y = 3x - 2 that passes through the point (2, 5)?

Options:

Correct Answer: y = 3x + 1

Solution:

Since parallel lines have the same slope, the equation is y - 5 = 3(x - 2) which simplifies to y = 3x + 1.

What is the equation of the line parallel to y = 3x - 2 that passes through the point (2, 5)?

What is the equation of the line parallel to y = 3x - 2 that passes through the point (2, 5)?

Step 1: Identify the slope of the given line y = 3x - 2. The slope (m) is 3.
Step 2: Since parallel lines have the same slope, the slope of the new line will also be 3.
Step 3: Use the point (2, 5) that the new line passes through. This point gives us x = 2 and y = 5.
Step 4: Use the point-slope form of the equation of a line, which is y - y1 = m(x - x1). Here, (x1, y1) is (2, 5) and m is 3.
Step 5: Substitute the values into the point-slope form: y - 5 = 3(x - 2).
Step 6: Simplify the equation. Start by distributing the 3: y - 5 = 3x - 6.
Step 7: Add 5 to both sides to isolate y: y = 3x - 6 + 5.
Step 8: Combine like terms: y = 3x - 1.

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