Final answer:
The equation of the straight line passing through point E(9, -2) and perpendicular to y = -3/2x + 5/2 is y = 2/3x - 8.
Step-by-step explanation:
To find the equation of the line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. The slope of the given line is -3/2, so the slope of the line perpendicular to it will be 2/3. Since the line passes through the point (9, -2), we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values, we get:
y - (-2) = 2/3(x - 9)
y + 2 = 2/3x - 6
y = 2/3x - 6 - 2
y = 2/3x - 8
Therefore, the equation of the straight line passing through point E(9, -2) and perpendicular to the line y = -3/2x + 5/2 is y = 2/3x - 8.