Final answer:
The equation of the line perpendicular to 5x - y = 7 and passing through the point (9, 1) is x + 5y = 14 in Standard Form.
Step-by-step explanation:
The student has asked for the equation of a line perpendicular to 5x - y = 7 that passes through the point (9, 1) in Standard Form. To find this equation, we first need to determine the slope of the given line. By writing the equation in slope-intercept form, we get y = 5x - 7, which implies a slope (m) of 5. Since the slope of a line perpendicular to this one would be the negative reciprocal, the perpendicular slope is -1/5.
Now, using the point-slope form of a line: y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point (9, 1), we substitute the values to get: y - 1 = (-1/5)(x - 9). Distributing the slope and rearranging terms to get the Standard Form yields: x + 5y = 14.