Answer:
Below
Step-by-step explanation:
The line L has the following equation:
● 2x - 3y = 5
Add -2x to both sides
● 2x - 3y -2x = 5 - 2x
● -3y = 5 - 2x
Multiply both sides by -1
● (-1) × -3y = (-1) × (5-2x)
● 3y = 2x - 5
Divide both sides by 3
● 3y/3 = (2x - 5)/3
● y = (2/3)x - 5/3
The line M is perpendicular to L
So the product of their slopes is -1
Let m be the slope of M
● m × (2/3) = -1
● m = -1 × (3/2)
● m = -3/2
So the equation of M is:
● y = (-3/2)x + b
b is the y-intercept
M passes through (2, -10)
Replace by the coordinates of this point
● -10 = (-3/2)×2 + b
● -10 = -3 + b
● b = -10 + 3
● b = -7
The equation of M is
● y = (-3/2)x -7
