Find the equation of the perpendicular at the point (4,3) to the line y + 2x = 5

To find the equation of the perpendicular at the point (4,3) to the line y + 2x = 5, we need to follow these steps: 1. Determine the slope of the given line: To do this, we can rearrange the equation y + 2x = 5 into slope-intercept form, y = -2x + 5. Thus, the slope of this line is -2. 2. Determine the slope of the perpendicular line: The slopes of perpendicular lines are negative reciprocals of each other. Therefore, the slope of the perpendicular line is 1/2. 3. Use the point-slope form of a line to write the equation of the perpendicular line: The point-slope form of a line is y - y1 = m(x - x1), where m is the slope of the line, and (x1, y1) is a point on the line. Since we know the slope of the perpendicular line is 1/2 and it passes through the point (4,3), we can substitute these values into the point-slope form to get y - 3 = 1/2(x - 4). 4. Simplify the equation: We can simplify the equation by multiplying both sides by 2 to eliminate the fraction, giving us 2y - 6 = x - 4. Then, we can rearrange it into standard form, which is Ax + By = C, by adding 4 to both sides and switching the positions of x and y to get 2y + x = 10. Therefore, the equation of the perpendicular at the point (4,3) to the line y + 2x = 5 is 2y + x = 10, which is option (D).