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:BelowStep-by-step explanation:The line L has the following equation: ● 2x - 3y = 5Add -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