equation of the line perpendicular to y=6/5x+ 7 that passes through the point & (−3, 2).

Answer 1

Perpendicular lines have opposite reciprocal slope.

1. Opposite means that the sign changes (positive becomes negative, negative becomes positive)
2. 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 - y₁ = m * (x - x₁)

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

Answer 2

Slope of the perpendicular line must be the inverse and have opposite sign

m = -5/6

Now apply the points to the equation to get the y-intercept

2 = -5/6(-3)+b

2 = +15/6+b

4/2 - 5/2 = b

b = -1/2

Y = -5/6*x-1/2