Find the equation of the line parallel to y = 3x + 2 and passing through (4, 5).

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Question: Find the equation of the line parallel to y = 3x + 2 and passing through (4, 5).

Options:

Correct Answer: y = 3x - 7

Solution:

Since the line is parallel, it has the same slope. Using point-slope form: y - 5 = 3(x - 4) gives y = 3x - 7.

Find the equation of the line parallel to y = 3x + 2 and passing through (4, 5).

Find the equation of the line parallel to y = 3x + 2 and passing through (4, 5).

Step 1: Identify the slope of the given line y = 3x + 2. The slope (m) is 3.
Step 2: Since the new line is parallel, it will have the same slope, which is also 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 (4, 5).
Step 4: Substitute the values into the point-slope form: y - 5 = 3(x - 4).
Step 5: Simplify the equation. Distribute 3: y - 5 = 3x - 12.
Step 6: Add 5 to both sides to solve for y: y = 3x - 12 + 5.
Step 7: Combine like terms: y = 3x - 7.

Slope of a Line – Understanding that parallel lines have the same slope.
Point-Slope Form – Using the point-slope form of a line equation to find the equation of a line given a point and slope.