Write the equation for the line that is perpendicular to y=3x-5 and passes through the point (3,2)

Question

Write the equation for the line that is perpendicular to y=3x-5 and passes through the point (3,2)

Answer 1

We are starting with y = 3x -5 which is the slope intercept form (y = mx +b) of a linear equation where the slope is m and the y intercept is b.  In this equation the slope m = 3

 

A perpendicular line would have a slope that is the negative reciprocal so the slope of the perpendicular line would be m = -1/3

 

So we have a slope m = -1/3   and a point (3,2)  so use the point slope formula (Y-Y₁) = m(X-X₁)

In this case (X1,Y1) = (3,2)

 

(Y - 2) = (-1/3)(X-3)

 

Y-2 = (-1/3)X + 1

 

Y = (-1/3)X + 3 would be the equation of the perpendicular line through (3,2)