y = 6/5x - ³/₅
Step-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 6/5
- The equation of the perpendicular line will be y = 6/5x + c
- We 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 / 2
12/5 = y + 3
2 ²/₅ – 3 = y
-³/₅ = y
- We can then replace the unknown value of C in our equation (y = 6/5x + c) with -3/5
y = 6/5x - ³/₅
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