Find the equation of the line that passes through the point (4, 5) and is perpen

Find the equation of the line that passes through the point (4, 5) and is perpendicular to the line y = 1/3x + 2.

Find the equation of the line that passes through the point (4, 5) and is perpendicular to the line y = 1/3x + 2.

Step 1: Identify the slope of the given line. The equation of the line is y = 1/3x + 2. The slope (m) is 1/3.
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 1/3 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 (4, 5) and m is -3.
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 isolate y: y = -3x + 12 + 5.
Step 7: Combine the constants: y = -3x + 17.

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.