Q:

Write an equation that is perpendicular to y=-5/6x+6 that goes through a point (-2,-3)

Accepted Solution

A:
y = 6/5x - ³/₅Step-by-step explanation:We understand that the gradient of a line perpendicular to another is negative reciprocal of the line it is perpendicular to;Therefore if the gradient of the line, from the equation, is -5/6, the gradient of the perpendicular line will be 6/5The equation of the perpendicular line will be y = 6/5x + cWe can use the point which it passes given as -  (-2,-3) -to find the y-intercept of the perpendicular line; AT y-intercept, the x value is usually 0 so we can derive the other point as;(-2, -3) (0, y)We know the formula of getting the gradient is;Gradient = (y² – y¹) / (x² – x¹) 6/5 = y - -3 / 0 – -2 6/5 = y + 3 / 212/5 = y + 32 ²/₅ – 3 = y-³/₅ = yWe can then replace the unknown value of C in our equation (y = 6/5x + c) with -3/5 y = 6/5x - ³/₅Learn More: