Final answer:
The linear equation in point-slope form that is perpendicular to y=5x-2 and passes through (4,7) is y=-1/5x+9.
Step-by-step explanation:
To find a linear equation that is perpendicular to y=5x-2 and passes through the point (4,7), 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 5. The negative reciprocal of 5 is -1/5. Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values to get the equation
y - 7 = -1/5(x - 4).
Simplifying this equation gives us the answer y = -1/5x + 9, option a.