Find the equation of the line parallel to y = 3x + 2 that passes through the poi

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Question: Find the equation of the line parallel to y = 3x + 2 that passes through the point (4, 1).

Options:

Correct Answer: y = 3x - 11

Solution:

Since the line is parallel, it has the same slope (3). Using point-slope form: y - 1 = 3(x - 4) gives y = 3x - 11.

Find the equation of the line parallel to y = 3x + 2 that passes through the point (4, 1).

Find the equation of the line parallel to y = 3x + 2 that passes through the point (4, 1).

Step 1: Identify the slope of the given line y = 3x + 2. The slope (m) is 3.
Step 2: Since the new line is parallel to the given line, it will have the same slope, which is 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 (4, 1).
Step 4: Substitute the slope (m = 3) and the point (4, 1) into the point-slope form: y - 1 = 3(x - 4).
Step 5: Simplify the equation. Start by distributing the 3: y - 1 = 3x - 12.
Step 6: Add 1 to both sides to solve for y: y = 3x - 12 + 1, which simplifies to y = 3x - 11.
Step 7: The final equation of the line parallel to y = 3x + 2 that passes through the point (4, 1) is y = 3x - 11.

Parallel Lines – Understanding that parallel lines have the same slope.
Point-Slope Form – Using the point-slope form of a line equation to find the equation of a line given a point and slope.