Answer: 2y + 3x - 16 = 0
Step-by-step explanation:
Equation of the line is y = 2x/3 - 5
From the equation , the slope m₁ = 2/3. therefore recall, from condition for perpendicularity, m₁m₂ = -1
The product of their gradient must be (-1).
Now since m₁ = 2/3 and m₁m₂ =-1
2m₂/3 = -1
Therefore , m₂ = -3/2.
Since the equation passes through the coordinate of (6,-1)
we now substitute for x and y in the equation of a line to get the y intercept (c)
y = mx + c
-1 = -3x/2 +c
-1 = -3/2 x 6 + c
-1 = -9 + c
-1 + 9 = c
Therefore c = 8
Now to get the equation of line that is perpendicular to y = 2x/3 - 5
y = -3x/2 + 8
making it a linear equation,
2y = -3x + 16
2y +3x - 16 = 0
