Respuesta :
The equation will be y = -3x +17 which pass through the point (5,2) and is perpendicular to the line -x + 3y =12.
To write this equation,
We determine the slope by solving the equation for y.
-x +3y = 12
⇒ 3y = 12 + x
⇒ y = 12 + x/ 3 ---------------------------- (1)
Dividing the equation (1) by 3
y = 4 + 1/3 x
we can rearrange the above equation,
y = 1/3 x + 4 ----------------------------- (2)
The slope of the line 1/3 . we need to know the slope of line perpendicular to this line. We find the negative reciprocal, -3 and use this as the slope for the perpendicular line.
We substitute 3 for m , 5 for x and 2 for y and solve for b:
y = mx + b
⇒ 2 = (-3) × 5 + b
⇒ 2 = -15 +b
⇒ b = 17
Therefore, the equation will be y = (-3)x + 17.
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