Final answer:
To find a perpendicular line to the given line and passing through a given point, we can use the negative reciprocal of the slope and the point-slope form equation.
Step-by-step explanation:
To find the equation of a line that is perpendicular to the line y=7/2x+3 and passes through the point (-7,5), we need to find the negative reciprocal of the slope of the given line. The given line has a slope of 7/2, so the perpendicular line will have a slope of -2/7.
Using the point-slope form of a linear equation, we can write the equation of the perpendicular line as: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Plugging in the values, we get: y - 5 = -2/7(x - (-7)). Simplifying the equation gives us the equation of the perpendicular line as: y = -2/7x + 9/7.