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What is the equation of the line parallel to y = 2x + 1 that passes through the
What is the equation of the line parallel to y = 2x + 1 that passes through the point (3, 4)?
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Q1
What is the equation of the line parallel to y = 2x + 1 that passes through the point (3, 4)?
y = 2x + 2
y = 2x + 1
y = 2x + 3
y = 2x - 2
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Parallel lines have the same slope, so y - 4 = 2(x - 3) => y = 2x - 2.
Questions & Step-by-step Solutions
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Q
Q: What is the equation of the line parallel to y = 2x + 1 that passes through the point (3, 4)?
Solution:
Parallel lines have the same slope, so y - 4 = 2(x - 3) => y = 2x - 2.
Steps: 6
Show Steps
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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