Answer:
y = -2/3x +4
Explanation:
You want the slope-intercept form equation for the line through point (-9, 10) and perpendicular to y = 3/2x -1/2.
Slope
The perpendicular line will have a slope that is the opposite reciprocal of the slope of the given line. The slope of the given line is the coefficient of x, 3/2. Then the perpendicular line will have slope ...
m = -1/(3/2) = -2/3
Intercept
The y-intercept of the line can be found from ...
y = mx +b
b = y -mx = 10 -(-2/3)(-9) = 10 -6 = 4
Equation
The equation you want is ...
y = mx +b
y = -2/3x +4
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Additional comment
The equation can also be found by starting with the point-slope form and rearranging.
y -10 = -2/3(x +9)
y = -2/3x -6 +10 = -2/3x +4
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