What is the equation of the line parallel to y = 3x - 5 that passes through the

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Question: What is the equation of the line parallel to y = 3x - 5 that passes through the point (2, 1)?

Options:

Correct Answer: y = 3x - 8

Solution:

Since the lines are parallel, they have the same slope. Using point-slope form: y - 1 = 3(x - 2) gives y = 3x - 8.

What is the equation of the line parallel to y = 3x - 5 that passes through the point (2, 1)?

What is the equation of the line parallel to y = 3x - 5 that passes through the point (2, 1)?

Step 1: Identify the slope of the given line y = 3x - 5. The slope (m) is 3.
Step 2: Since we need a line parallel to this one, it will also have a slope of 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 (2, 1) and m is 3.
Step 4: Substitute the values into the point-slope form: y - 1 = 3(x - 2).
Step 5: Simplify the equation. First, distribute the 3: y - 1 = 3x - 6.
Step 6: Add 1 to both sides to isolate y: y = 3x - 6 + 1.
Step 7: Combine like terms: y = 3x - 5.

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