Question

Find the equation of The line perpendicular to Y= -2+3/5X passing through the points (3, -4)

Answer 1

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

Explanation:

The line (a) passing through point (3, -4) is perpendicular to line (b) whose equation is; y = -2 +
`(3)/(5)`x

The slope of line (b) =
`(3)/(5)`

For perpendicular lines, the product of their slopes = -1

So line (a) has a slope of: -1 ÷
`(3)/(5)` = -
`(5)/(3)`

Taking another point (x,y) on line (a);

Slope = change in y ÷ change in x

`(y - -4)/(x - 3)` = -
`(5)/(3)`

y + 4 =
`(5)/(3)`(x - 3)

y = -
`(5)/(3)`x + 5 - 4

y = -
`(5)/(3)`x + 1

Finally,

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