Perpendicular lines have opposite reciprocal slope.

- Opposite means that the sign changes (positive becomes negative, negative becomes positive)
- Reciprocal means that the fraction flips (swap the numerator and denominator)

The line y = (6/5)*x + 7 is in the format y = m*x + b where m is the slope.

If the slope of this line is 6/5, then the slope of the perpendicular line (opposite reciprocal) is -5/6.

We can know use point-slope form to write the equation of perpendicular line passing through the point (-3,2):

y - y_{1} = m * (x - x_{1})

y - 2 = (-5/6) * (x - (-3))

y - 2 = (-5/6) * (x + 3)

If you need the equation in slope-intercept form like the original:

y - 2 = (-5/6) * (x + 3)

y - 2 = (-5/6)*x + (-5/6)*3

y - 2 = (-5/6)*x + -5/2

y = (-5/6)*x + -5/2 + 2

y = (-5/6)*x + -5/2 + 4/2

y = (-5/6)*x + -1/2

y = (-5/6)*x - 1/2