Final answer:
To find an equation of a line that is perpendicular to line p, we first calculate the slope of line p using the given points. The slope of line p is -1/2, so the slope of the perpendicular line is the negative reciprocal of -1/2, which is 2. An equation for the perpendicular line is y = 2x + b, where b is the y-intercept.
Step-by-step explanation:
To find the equation of a line that is perpendicular to line p, we first need to determine the slope of line p. We can use the points (9,7) and (13,5) to do this. The slope (m) is calculated by taking the difference in y-coordinates divided by the difference in x-coordinates:
m = (y2 - y1) / (x2 - x1)
In this case, m = (5 - 7) / (13 - 9) = -2 / 4 = -1/2. A line perpendicular to line p will have a slope that is the negative reciprocal of -1/2, which is 2. The equation of a line with a slope of 2 can be written in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Without the y-intercept, the specific equation cannot be determined, but a general form of the equation can be: y = 2x + b.
Therefore, an equation that represents a line perpendicular to line p could be y = 2x + b, where b is the y-intercept that would be determined based on a specific point on the perpendicular line.