What is the equation of the line parallel to y = 3x + 4 that passes through the

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Question: What is the equation of the line parallel to y = 3x + 4 that passes through the point (0, -2)?

Options:

Correct Answer: y = 3x - 2

Solution:

Parallel lines have the same slope. The slope is 3, so using point-slope form: y + 2 = 3(x - 0) => y = 3x - 2.

What is the equation of the line parallel to y = 3x + 4 that passes through the point (0, -2)?

What is the equation of the line parallel to y = 3x + 4 that passes through the point (0, -2)?

Correct Answer: y = 3x - 2

Step 1: Identify the slope of the given line. The equation is y = 3x + 4, so the slope (m) is 3.
Step 2: Since parallel lines have the same slope, the slope of the new line will also be 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 (0, -2).
Step 4: Substitute the values into the point-slope form: y - (-2) = 3(x - 0).
Step 5: Simplify the equation: y + 2 = 3x.
Step 6: Solve for y by subtracting 2 from both sides: y = 3x - 2.

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