Find the equation of the line that passes through (2, 3) and is perpendicular to

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Question: Find the equation of the line that passes through (2, 3) and is perpendicular to the line y = 1/3x + 2.

Options:

Correct Answer: y = -3x + 9

Solution:

The slope of the given line is 1/3, so the perpendicular slope is -3. Using point-slope form, y - 3 = -3(x - 2) gives y = -3x + 9.

Find the equation of the line that passes through (2, 3) and is perpendicular to the line y = 1/3x + 2.

Find the equation of the line that passes through (2, 3) and is perpendicular to the line y = 1/3x + 2.

Step 1: Identify the slope of the given line. The equation is y = 1/3x + 2, so the slope (m) is 1/3.
Step 2: Find the slope of the line that is perpendicular to the given line. The perpendicular slope is the negative reciprocal of 1/3, which is -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 (2, 3) and m is -3.
Step 4: Substitute the values into the point-slope form: y - 3 = -3(x - 2).
Step 5: Simplify the equation. Distribute -3: y - 3 = -3x + 6.
Step 6: Add 3 to both sides to solve for y: y = -3x + 6 + 3, which simplifies to y = -3x + 9.

Slope of a Line – Understanding how to find the slope from the equation of a line and how to determine the slope of a perpendicular line.
Point-Slope Form – Using the point-slope form of a linear equation to find the equation of a line given a point and a slope.