Final answer:
The equation of the line that is perpendicular to f(x) = -5x - 7 and passes through (2, 3) is y = 1/5x + 13/5.
Step-by-step explanation:
The question asks us to find the equation of a line that is perpendicular to the given line f(x) = -5x - 7 and passes through the point (2, 3).
First, we determine the slope of the given line. Since the slope of f(x) is -5, the slope of a line perpendicular to it will be the negative reciprocal. Therefore, the slope of the line we are trying to find is 1/5.
Next, we use the point-slope form of the line equation y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through. Substituting the slope and point (2, 3), we get:
y - 3 = 1/5(x - 2)
After simplifying, we find the equation of the line:
y - 3 = 1/5x - 2/5
y = 1/5x + 13/5