What is the equation of the line that is perpendicular to y=2/3x-5 and passes through (6,-1) ?

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