What is the equation of the line parallel to y = 2x + 1 that passes through the

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

Options:

Correct Answer: y = 2x + 2

Solution:

Parallel lines have the same slope, so y - 4 = 2(x - 3) => y = 2x - 2.

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

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

Step 1: Identify the slope of the given line. The equation is y = 2x + 1, so the slope (m) is 2.
Step 2: Since parallel lines have the same slope, the slope of the new line will also be 2.
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 (3, 4) and m is 2.
Step 4: Substitute the values into the point-slope form: y - 4 = 2(x - 3).
Step 5: Simplify the equation. Distribute the 2: y - 4 = 2x - 6.
Step 6: Add 4 to both sides to solve for y: y = 2x - 2.

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