the line through A(-3,-2) and B(4,y) is perpendicular to a line with slope 7/3. find y

Question

A(-3,-2) and B(4,y) is perpendicular to a line 7/3. find y

Answer 1

A(-3,-2) and B(4,y)

Slope say m1 =( y2-y1)/(x2-x1)

m1 =  (y+2)/4+3

m1 = (y+2)/7

The line through A,B  is perpendicular to another line .

the line slope is given say m2 = 7/3

We know that m1*m2 = -1

(y+2)/7 *7/3 = -1

(y+2)/3 = -1

Multiply to each side by3.

3(y+2)/3 = -1*3

y+2 = -3

Subtract 2 from each side.

y+2-2 = -3-2

⇒ y = -5