Answer:
y = −3x/2 − 3/2
Explanation:
The equation of the line in the slope-intercept form is y=2x/3 + 1
The perpendicular slope ( m1) is negative reciprocal of the slope m
m1 = -1/m = -1 divide by 2/3 = -3/2
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: −6 = (−3/2) ⋅ (3) + a
Thus, a = −3/2
Therefore, the equation of the line is y = −3x/2 − 3/2
heres a picture of the graph