Final answer:
The equation of the line passing through the point (4,3) and perpendicular to the line 4x - y = 5 is y= -1/4x + 4.
Step-by-step explanation:
To find the equation of the line that passes through the point (4,3) and is perpendicular to the line 4x - y = 5, we first need to determine the slope of the given line. The equation 4x - y = 5 can be rewritten in slope-intercept form as y = 4x - 5, which reveals that the slope is 4. Since perpendicular lines have slopes that are negative reciprocals of each other, the slope of the line we're looking for is -1/4.
Next, we use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Plugging in our slope -1/4 and the point (4,3), we get y - 3 = -1/4(x - 4). Simplifying this equation, we get y - 3 = -1/4x + 1. Adding 3 to both sides, we get y = -1/4x + 4 as the equation of the line that is perpendicular to 4x - y = 5 and passes through (4,3).