find the slope of a line?

Question

find the slope of the line through (6,1) and perpendicular to y =3/2x + 1/4

Answer 1

Standerd form equation y = mx+b

y = 3/2x+1/4

Slope of the line m1 = 3/2

Line equation to through (6,1) and its slope say m2

y-y1 = m2(x-x1)

y-1 = m2(x-6)

We know that perpendicular line and given line slopes product  be -1

m1*m2 = -1

3/2*m2 = -1

Multiply 2/3 to each side.

3/2*2/3*m2 = -1*2/3

m2 = -2/3

Slope of perpendicular line through (6,1) m2 = -2/3