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.
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Answer:BelowStep-by-step explanation:The line L has the following equation: β 2x - 3y = 5Add -2x to both sides β 2x - 3y -2x = 5 - 2x β -3y = 5 - 2x Multiply both sides by -1 β (-1) Γ -3y = (-1) Γ (5-2x)β 3y = 2x - 5 Divide both sides by 3 β 3y/3 = (2x - 5)/3 β 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 β m Γ (2/3) = -1 β m = -1 Γ (3/2) β m = -3/2 So the equation of M is:β y = (-3/2)x + b b is the y-intercept M passes through (2, -10) Replace by the coordinates of this point β -10 = (-3/2)Γ2 + b β -10 = -3 + bβ b = -10 + 3 β b = -7 The equation of M is β y = (-3/2)x -7