What is the equation of the line parallel to y = 4x - 5 that passes through the point (2, 3)?
Correct Answer: y = 4x - 5
- 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 isolate y: y = 4x - 8 + 3.
- Step 7: Combine like terms: y = 4x - 5.
- Step 8: The equation of the line parallel to y = 4x - 5 that passes through the point (2, 3) is y = 4x - 5.
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