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 (1, 1)?

Options:

Correct Answer: y = 3x - 1

Solution:

Parallel lines have the same slope, so y - 1 = 3(x - 1) => y = 3x - 1.

What is the equation of the line parallel to y = 3x + 2 that passes through the point (1, 1)?

What is the equation of the line parallel to y = 3x + 2 that passes through the point (1, 1)?

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-slope form of the equation of a line, which is y - y1 = m(x - x1). Here, (x1, y1) is the point (1, 1) and m is 3.
Step 4: Substitute the values into the point-slope form: y - 1 = 3(x - 1).
Step 5: Simplify the equation: y - 1 = 3x - 3.
Step 6: Add 1 to both sides to solve for y: y = 3x - 2.

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