What is the equation of the line parallel to y = 3x - 2 and passing through the

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

Options:

Correct Answer: y = 3x + 1

Solution:

The slope of the given line is 3. Using point-slope form: y - 5 = 3(x - 2) gives y = 3x + 1.

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

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

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

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