To find the equation of a line perpendicular to a given line, you need to determine the negative reciprocal of the slope of the given line.
In this case, the given line is y = -5/3x + 11 1/3. The slope of this line is -5/3. The negative reciprocal of -5/3 is 3/5.
Next, you have a point P(-2,3) that the perpendicular line must pass through.
Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) represents the coordinates of a point on the line and m represents the slope, you can substitute the values into the equation.
Therefore, for the equation of the line perpendicular to y = -5/3x + 11 1/3 and containing P(-2,3), the correct answer would be:
y - 3 = 3/5(x - (-2))
Simplifying this equation, you get:
y - 3 = 3/5(x + 2)
So, the correct answer for the equation of the line would be:
y = 3/5x + 6/5
Based on the options given, it seems that none of the provided answers match the correct equation.