Answer:
y = 3x/2 + 6
Step-by-step explanation:
Find the equation of the line perpendicular to the line 2x + 3y = 5 passing through the point (−2,3).
The equation of the line in the slope-intercept form is y = 5/3 − 2x/3.
The slope of the perpendicular line is negative inverse: m = 3/2.
So, the equation of the perpendicular line is y = 3x/2 + a.
To find a, we use the fact that the line should pass through the given point:
3 = (3/2) ⋅ (−2) + a.
Thus, a = 6.
Therefore, the equation of the line is y = 3x/2 + 6.
Answer: y = 3x/2 + 6
