Question

Line L has equation 2x - 3y = 5. Line M passes through the point (2, -10) and is perpendicular to line L. Determine the equation for line M.

Answer 1

Below

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