Find the equation of the line that is perpendicular to y = 5x + 2 and passes thr

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Question: Find the equation of the line that is perpendicular to y = 5x + 2 and passes through (2, 3).

Options:

Correct Answer: y = -5x + 13

Solution:

The slope of the perpendicular line is -1/5. Using point-slope form: y - 3 = -1/5(x - 2) gives y = -1/5x + 13/5.

Find the equation of the line that is perpendicular to y = 5x + 2 and passes through (2, 3).

Find the equation of the line that is perpendicular to y = 5x + 2 and passes through (2, 3).

Step 1: Identify the slope of the given line y = 5x + 2. The slope (m) is 5.
Step 2: Find the slope of the line that is perpendicular to the given line. The slope of a perpendicular line is the negative reciprocal of the original slope. So, the negative reciprocal of 5 is -1/5.
Step 3: Use the point-slope form of a line equation, which is y - y1 = m(x - x1). Here, (x1, y1) is the point (2, 3) and m is -1/5.
Step 4: Substitute the values into the point-slope form: y - 3 = -1/5(x - 2).
Step 5: Simplify the equation. Distribute -1/5: y - 3 = -1/5x + 2/5.
Step 6: Add 3 to both sides to solve for y: y = -1/5x + 2/5 + 3.
Step 7: Convert 3 to a fraction with a denominator of 5: 3 = 15/5. Now, add: y = -1/5x + 2/5 + 15/5.
Step 8: Combine the fractions: y = -1/5x + 17/5.

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