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

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Question: What is the equation of a line parallel to y = -3x + 2 that passes through the point (1, 4)?

Options:

Correct Answer: y = -3x + 7

Solution:

Parallel lines have the same slope. The slope is -3. Using point-slope form: y - 4 = -3(x - 1) gives y = -3x + 7.

What is the equation of a line parallel to y = -3x + 2 that passes through the point (1, 4)?

What is the equation of a line parallel to y = -3x + 2 that passes through the point (1, 4)?

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

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