What is the equation of the line parallel to y = 4x - 5 and passing through (2,

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Question: What is the equation of the line parallel to y = 4x - 5 and passing through (2, 3)?

Options:

Correct Answer: y = 4x - 1

Solution:

Parallel lines have the same slope. Using point-slope form: y - 3 = 4(x - 2) => y = 4x - 5.

What is the equation of the line parallel to y = 4x - 5 and passing through (2, 3)?

What is the equation of the line parallel to y = 4x - 5 and passing through (2, 3)?

Step 1: Identify the slope of the given line y = 4x - 5. The slope (m) is 4.
Step 2: Since parallel lines have the same slope, the slope of the new line will also be 4.
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, 3).
Step 4: Substitute the values into the point-slope form: y - 3 = 4(x - 2).
Step 5: Simplify the equation: y - 3 = 4x - 8.
Step 6: Add 3 to both sides to solve for y: y = 4x - 5.

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