Final answer:
To find a line perpendicular to y = (3/2)x - 4 that passes through the point (6,5) and has a negative reciprocal slope, we can derive the equation using the slope-intercept form. The equation of the line perpendicular to y = (3/2)x - 4 and passing through (6,5) is y = (-2/3)x + 17.
Step-by-step explanation:
To find a line perpendicular to y = (3/2)x - 4 and passing through the point (6,5), we need to determine the slope of the given line and then find the negative reciprocal of that slope. The given line has a slope of 3/2. The negative reciprocal of 3/2 is -2/3. So, the equation of the line perpendicular to y = (3/2)x - 4 and passing through (6,5) is y = (-2/3)x + b, where b is the y-intercept.
To find the value of b, substitute the coordinates of the given point into the equation. We get 5 = (-2/3)(6) + b. Simplifying this equation, we find b = 17. Therefore, the equation of the line perpendicular to y = (3/2)x - 4 and passing through (6,5) is y = (-2/3)x + 17.